Pre-AP Precalculus Module 7 Triangle Applications

Pre-AP Precalculus

Module 7

Triangle Applications

7.1 Right Triangle Applications

Sullivan & Sullivan – Section 8.1

Example 1 – Find the exact value of the six trigonometric functions of the angle 𝜃 in the figure.

Example 2 – If 𝑏 = 2 and 𝐴 = 40°, find 𝑎, 𝑐, and 𝐵.

Example 3 – If 𝑎 = 3 and 𝑏 = 2, find 𝑐, 𝐴, and 𝐵.

Example 4 – A surveyor can measure the width of a river by setting up a transit at point 𝐶 on one side of

the river and taking a sighting of a point 𝐴 on the other side. After turning through an angle of 90° at 𝐶,

the surveyor walks a distance of 200 meters to point 𝐵. Using the transit at 𝐵, the angle at 𝐵 is measured

and found to be 20°. What is the width of the river rounded to the nearest meter?



Example 5 – A straight trail leads from the Alpine Hotel, elevation 8000 ft, to a scenic overlook, elevation

11,100 ft. The length of the trail is 14,100 feet. What is the inclination (grade or angle of elevation) of the

trail?

Example 6 – Meteorologists find the height of a cloud using an instrument called a ceilometer. A

ceilometer consists of a light projector that directs a vertical light beam up to the cloud base and a light

detector that scans the cloud to detect the light beam. On December 13, 2011, at Midway Airport in

Chicago, a ceilometer was employed to find the height of the cloud cover. It was set up with its light

detector 300 feet from its light projector. If the angle of elevation from the light detector to the base of

the cloud was 75°, what was the height of the cloud cover?

Example 7 – Adorning the top of the Board of Trade building in Chicago is a statue of Ceres, the Roman

goddess of wheat. From street level, two observations are taken 400 feet from the center of the building.

The angle of elevation to the base of the statue is found to be 55.1° and the angle of elevation to the top of

the statue is 56.5°. What is the height of the statue?



Example 8 – In operation since 1846, the Gibb’s Hill Lighthouse stands 117 feet high on a hill 245 feet

high, so its beam of light is 362 feet above sea level. A brochure states that the light can be seen on the

horizon about 26 miles from the lighthouse. Verify the accuracy of this statement. As a reminder, the

radius of Earth is 3960 miles.

In navigation and surveying, the direction or bearing from a point 𝑂 to a point 𝑃 equals the acute angle

between 𝑂𝑃⃗⃗⃗⃗ ⃗ and the north-south line.

Example 9 – What are the bearings from O to objects at (a) 𝑃1, (b) 𝑃2, (c) 𝑃3, and

(d) 𝑃4?

Example 10 – A Boeing 777 aircraft takes off from O’Hare Airport on runway 2 LEFT, which has a bearing

of N20°E. After flying for 1 mile, the pilot of the aircraft requests permission to turn 90° and head toward

the northwest. The request is granted. After the plane goes 2 miles in this

new direction, what bearing should the control tower use to locate the

aircraft?



Complete the following exercises on a separate sheet of paper.

In exercises 1 – 4, find the exact value of the six trigonometric functions of the angle 𝜽 in the

figure.

1.

2.

3.

4.

In exercises 5 – 8, find the exact value of each expression.

5. sin38° − cos 52°

6. cos10°

sin80°

7. 1 − cos2 20° − cos2 70°

8. tan 20° −cos70°

cos20°

In exercises 9 – 14, use the given right triangle to solve the triangle using the information given.

9. 𝑏 = 5, 𝐵 = 20°

10. 𝑎 = 6, 𝐵 = 40°

11. 𝑏 = 4, 𝐴 = 10°

12. 𝑎 = 5, 𝐴 = 25°

13. 𝑎 = 5, 𝑏 = 3

14. 𝑎 = 2, 𝑐 = 5

15. A person in a small boat, offshore from a vertical cliff known to be 100 feet in

height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 25°, how far are you

from the base of the plateau?

16. A 22-foot extension ladder leaning against a building makes a 70° angle with the ground. How far up the

building does the ladder touch?

17. At 10 AM, on April 26, 2009, a building 300 feet high casts a shadow 50 feet long. What was the angle of

elevation the Sun?

18. A state trooper is hidden 30 feet from a highway (this distance is measured perpendicularly to the

highway). One second after a truck passes the trooper, the angle 𝜃 between the highway and the line of

observation from the patrol car to the truck is measured.

a. If the angle measures 15°, how fast is the truck moving? Express the answer in miles per hour.

b. If the angle measures 20°, how fast is the truck moving? Express the answer in miles per hour.

c. If the speed limit is 55 miles per hour and a speeding ticket is issued for speeds of 5 miles per hour

or more over the limit, for what angles should the trooper issue a ticket?

19. A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of

depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from

the wall?



20. Situated between Portage Road and the Niagara Parkway directly across from the Canadian Horseshoe

Falls, the Falls Incline Railway is a funicular that carries passengers up an embankment to Table Rock

Observation Point. If the length of the track is 51.8 meters and the angle of inclination is 36°2’, determine

the height of the embankment.

21. A DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40°E. After flying for 1

2

mile, the pilot requests permission to turn 90° and head toward the southeast. The permission is granted.

After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the

aircraft?

22. A ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns

90° toward the south. After 2 hours, maintaining the same speed, what is the bearing to the ship from port?

23. Willis Tower in Chicago is the third tallest building in the world and is topped by a high antenna. A

surveyor on the ground makes the following measurement:

The angle of elevation from his position to the top of the building is 34°.

The distance from his position to the top of the building is 2593 feet.

The distance from his position to the top of the antenna is 2743 feet.

a. How far away from the base of the building is the surveyor located?

b. How tall is the building?

c. What is the angle of elevation from the surveyor to the top of the antenna?

d. How tall is the antenna?

24. A camera is mounted on a tripod 4 feet high at a distance of 10 feet from George, who is 6 feet tall. If the

camera lens has angles of depression and elevation of 20°, will George’s feet and head be seen by the lens?

If not, how far back will the camera need to be moved to include George’s feet and head?

25. A blimp suspended in the air at a height of 500 feet, likes directly over a line from Soldier Field to the Adler

Planetarium on Lake Michigan. If the angle of depression from the blimp to the stadium is 32° and from the

blimp to the planetarium is 23°, find the distance between Soldier Field and the Adler Planetarium.

26. One World Trade Center is to be the centerpiece of the rebuilding of the World Trade Center in New York

City. The tower will be 1368 feet tall (not including the broadcast antenna). The angle of elevation from the

base of an office building to the top of the tower is 34°. The angle of elevation from the helipad on the roof

of the office building to the top of the tower is 20°.

a. How far away is the office building from One World Trade Center? Assume the side of the tower is

vertical. Round to the nearest foot.

b. How tall is the office building? Round to the nearest foot.

7.2 The Law of Sines


Non-right triangles are known as oblique triangles. In geometry, you learned about the SSS, SAS, AAS,

and ASA triangle congruence theorems. Given measurements corresponding to one of these four

patterns, we can solve an oblique triangle by finding all the missing side lengths and angle

measurements. It’s also important to note that in the study of Oblique Triangles, the angles are labeled

with capital letters, while the side opposite each angle is labeled with the corresponding lower case

letter. Thus side 𝑎 is opposite angle 𝐴.

Law of Sines

For a triangle with sides 𝑎, 𝑏, 𝑐 and opposite angles 𝐴, 𝐵, 𝐶, respectively, sin𝐴

𝑎=

sin𝐵

𝑏=

sin𝐶

𝑐.

The Law of Sines should only be used when solving AAS and ASA triangles.

The Law of Sines should never be used to calculate an angle, as this would require the use of arcsine, and

the output of arcsine has a maximum value of 90°, excluding any possible obtuse angles.

The sum of the interior angles of any triangle is 180°.

Example 1 – Prove the Law of Sines.

Example 2 – Solve the triangle: 𝐴 = 40°, 𝐵 = 60°, 𝑎 = 4.

Example 3 – Solve the triangle: 𝐴 = 35°, 𝐵 = 15°, 𝑐 = 5.



Example 4 – To measure the height of a mountain, a surveyor takes two sightings of the peak at a distance

900 meters apart on a direct line to the mount. The first observation results in an angle of elevation of

47°, and the second results in an angle of elevation of 35°. If the transit is 2 meters high, what is the

height of the mountain?

Example 5 - Coast Guard Station Zulu is located 120 miles due west of Station X-ray. A ship at sea sends

an SOS call that is received by each station. The call to Station Zulu indicates that the bearing of the ship

from Zulu is N40°E. The call to Station X-ray indicates that the bearing of the ship from X-ray is N30°W.

(a) How far is each station from the ship? (b) If a helicopter capable of flying 200 miles per hour is

dispatched from the nearer station to the ship, how long will it take to reach the ship?


In exercises 1 – 8, solve each triangle.

1. 𝐴 = 40°, 𝐵 = 20°, 𝑎 = 2

2. 𝐴 = 50°, 𝐶 = 20°, 𝑎 = 3

3. 𝐵 = 70°, 𝐶 = 10°, 𝑏 = 5

4. 𝐴 = 70°, 𝐵 = 60°, 𝑐 = 4

5. 𝐴 = 110°, 𝐶 = 30°, 𝑐 = 3

6. 𝐵 = 10°, 𝐶 = 100°, 𝑏 = 2

7. 𝐴 = 40°, 𝐵 = 40°, 𝑐 = 2

8. 𝐵 = 20°, 𝐶 = 70°, 𝑎 = 1



9. Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call

that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to

Station Baker indicates that the ship is located S60°E.

a. How far is each station from the ship?

b. If a helicopter capable of flying 200 mph is dispatched from the station nearest the ship, how long

will it take to reach the ship?

10. At exactly the same time, Tom and Alice measured the angle of elevation to the mood while standing

exactly 300 km apart. The angle of elevation to the moon for Tom was 49.8974°, and the angle of elevation

to the moon for Alice was 49.9312°. To the nearest 1000 km, how far was the moon from Earth when the

measurement was obtained?

11. An aircraft is spotted by two observers who are 1000 feet apart. As the airplane passes over the line

joining them, each observer takes a sighting of the angle of elevation to the plane, measured at 40° and 35°.

How high is the airplane?

12. The highest bridge in the world is the bridge over the Royal Gorge of the Arkansas River in Colorado.

Sightings to the same point at water level directly under the bridge are taken from each side of the 880-

foot-long bridge, with angles of depression measuring 69.2° and 65.5°. How high is the bridge?

13. Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby

fence. The angle of elevation of the tree from one position on a flat path from the tree is 30°, and from a

second position 40 feet farther along this path, it is 20°. What is the height of the tree?

14. A loading ramp 10 feet long that makes an angle of 18° with the horizontal is to be replaced by one that

makes an angle of 12° with the horizontal. How long is the new ramp?

15. Adam must fly home to St. Louis from a business meeting in Oklahoma City. One flight option flies directly

to St. Louis, a distance of about 461.1 miles. A second flight option flies first to Kansas City and then

connects to St. Louis. The bearing from Oklahoma City to Kansas City is N29.6°E and the bearing from

Oklahoma City to St. Louis is N57.7°E. The bearing from St. Louis to Oklahoma City is S57.7°W, and the

bearing from St. Louis to Kansas City is N79.4°W. How many more frequent flier miles will Adam receive if

he takes the connecting flight rather than the direct flight?

16. An awning mounted directly above a sliding glass door that is 88 inches tall forms an angle of 50° with the

glass door. The purpose of the awning is to prevent sunlight from entering the house when the angle of

elevation of the Sun is more than 65°. Find the length 𝐿 of the awning.

7.3 The Law of Cosines and Area of a Triangle

Sullivan & Sullivan – Sections 8.3 & 8.4

We will use the Law of Cosines to solve SSS (three sides are known) and SAS (two sides and the included

angle are known) triangles. In an SSS triangle, the two shorter sides must have a sum greater than the

longest side, otherwise the measurements do not describe an actual triangle. If a triangle has two sides

that are known with a known angle opposite one of the two sides, this is an SSA triangle. We say that an

SSA triangle falls into the ambiguous case, which we will discuss in the next section.

Law of Cosines

𝑐2 = 𝑎2 + 𝑏2 − 2𝑎𝑏 cos𝐶

𝑏2 = 𝑎2 + 𝑐2 − 2𝑎𝑐 cos 𝐵

𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 cos 𝐴

Notice that all three formulas are the same. The angle in the formula is opposite the squared side on the

left side of the equation.

Example 1 – Prove the Law of Cosines.

Example 2 – Rearrange 𝑐2 = 𝑎2 + 𝑏2 − 2𝑎𝑏 cos 𝐶 to solve for angle 𝐶.

Example 3 – Solve the triangle: 𝑎 = 2, 𝑏 = 3, 𝐶 = 60°.



Example 4 – Solve the triangle: 𝑎 = 4, 𝑏 = 3, 𝑐 = 6.

Example 5 – A motorized sailboat leaves Naples, Florida, bound for Key West, 150 miles away.

Maintaining a constant speed of 15 miles per hour, but encountering heavy crosswinds and strong

currents, the crew finds, after 4 hours, that the sailboat is off course by 20°. (a) How far is the sailboat

from Key West at this time? (b) Through what angle should the sailboat turn to correct its course? (c)

How much time has been added to the trip because of this? (Assume that the speed remains at 15 mph)

If one of the side lengths, 𝑏, of a triangle and the length of the altitude, ℎ, to that side are both known, the

area of the triangle can be calculated as 𝐴𝑟𝑒𝑎 =1

2𝑏ℎ.

In an SAS triangle with side lengths 𝑎 and 𝑏 as well as the included angle 𝐶 are known, the area of a

triangle can be calculated as 𝐴𝑟𝑒𝑎 =1

2𝑎𝑏 sin 𝐶. Similarly, we could calculate the area as 𝐴𝑟𝑒𝑎 =

1

2𝑏𝑐 sin𝐴

or 𝐴𝑟𝑒𝑎 =1

2𝑎𝑐 sin𝐵.

Example 6 – Prove 𝐴𝑟𝑒𝑎 =1

2𝑎𝑏 sin 𝐶 if 𝑎, 𝑏, and 𝐶 are known.



Example 7 – Find the area of the triangle for which 𝑎 = 8, 𝑏 = 6, and 𝐶 = 30°.

In an SSS triangle, we can calculate the area using Heron’s Formula: 𝐴𝑟𝑒𝑎 = √𝑠(𝑠 − 𝑎)(𝑠 − 𝑏)(𝑠 − 𝑐),

where 𝑠 =𝑎+𝑏+𝑐

2 is the semi-perimeter. Some texts refer to Heron’s formula as Hero’s formula.

Example 9 – Find the area of a triangle whose sides are 4, 5, and 7.

Example 11 – Find the area of a triangle for which 𝐴 = 30°, 𝐵 = 50°, and 𝑐 = 7.




For exercises 1 – 20, solve each triangle and calculate its area.

1. 𝑎 = 3, 𝑏 = 4, 𝐶 = 40°

2. 𝑎 = 2, 𝑐 = 1, 𝐵 = 10°

3. 𝑏 = 1, 𝑐 = 3, 𝐴 = 80°

4. 𝑎 = 6, 𝑏 = 4, 𝐶 = 60°

5. 𝑎 = 3, 𝑐 = 2, 𝐵 = 110°

6. 𝑏 = 4, 𝑐 = 1, 𝐴 = 120°

7. 𝑎 = 12, 𝑏 = 13, 𝑐 = 5

8. 𝑎 = 5, 𝑏 = 8, 𝑐 = 9

9. 𝑎 = 2, 𝑏 = 2, 𝑐 = 2

10. 𝑎 = 3, 𝑏 = 3, 𝑐 = 2

11. 𝑎 = 4, 𝑏 = 3, 𝑐 = 6

12. 𝑎 = 10, 𝑏 = 8, 𝑐 = 5

13. 𝐵 = 20°, 𝐶 = 75°, 𝑏 = 5

14. 𝐴 = 50°, 𝐵 = 55°, 𝑐 = 9

15. 𝑎 = 6, 𝑏 = 8, 𝑐 = 9

16. 𝐵 = 35°, 𝐶 = 65°, 𝑎 = 15

17. 𝑎 = 4, 𝑐 = 5, 𝐵 = 55°

18. 𝐴 = 65°, 𝐵 = 72°, 𝑏 = 7

19. 𝑏 = 5, 𝑐 = 12, 𝐴 = 60°

20. 𝑎 = 10, 𝑏 = 10. 𝑐 = 15



21. An airplane flies due north from Ft. Myers to Sarasota, a distance of 150 miles and then turns through an

angle of 50° eastward and flies to Orlando, a distance of 100 miles.

a. How far is it directly from Ft. Myers to Orlando?

b. What bearing should the pilot use to fly directly from Ft. Myers to Orlando?

22. A cruise ship maintains an average speed of 15 knots in going from San Juan, Puerto Rico, to Barbados,

West Indies, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan in

a direction of 20° off a direct heading to Barbados. The captain maintains the 15-knot speed for 10 hours,

after which time the path to Barbados becomes clear of storms.

a. Through what angle should the captain turn to head directly to Barbados?

b. Once the turn is made, how long will it be before the ship reaches Barbados if the same 15-knot

speed is maintained?

23. In attempting to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course

that was 10° in error.

a. If the aircraft maintains an average speed of 220 miles per hour and if the error in direction is

discovered after 15 minutes, through what angle should the pilot turn to head toward Louisville?

b. What new average speed should the pilot maintain so that the total time of the trip is 90 minutes?

24. A major League baseball diamond is actually a square 90 feet on a side. The pitching rubber is located 60.5

feet from home plate on a line joining home plat to second base.

a. How far is it from the pitching rubber to first base?

b. How far is it from the pitching rubber to second base?

c. If a pitcher faces home plate, through what angle does he need to turn to face first base?

25. The height of a radio tower us 500 feet, and the ground on one side of the tower slopes upward at an angle

of 10°.

a. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on

the sloped side 100 feet from the base of the tower?

b. How long should a second guy wire be if it is to connect to the middle of the tower and be secured

at a point 100 feet from the base of the tower on the flat side?

26. Find the area of the segment of a circle whose radius is 8 feet, formed by a central angle of 70°. Hint:

Subtract the area of the triangle from the area of the sector.

27. The dimensions of home plate at any major league baseball stadium are shown. Find

the area of home plate.



28. The figure shoes a circle of radius 𝑟 with center at 𝑂. Find the area of the shaded region

as a function of the central angle 𝜃.

29. Completed in 1902 in New York City, the Flatiron Building is triangular shaped and

bounded by 22nd Street, Broadway, and 5th Avenue. The building measures

approximately 87 feet on the 22nd Street side, 190 feet on the Broadway side, and 173

feet on the 5th Avenue side. Approximate the ground area covered by the building.

30. The Bermuda Triangle is roughly defined by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort

Lauderdale, Florida. The distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San

Juan to Hamilton are approximately 1028, 1046, and 965 miles, respectively. Ignoring the curvature of the

Earth, approximate the area of the Bermuda Triangle.

7.4 The Ambiguous Case

Sullivan & Sullivan – Section 8.2 Foerster – Section 6.5

If two side measurements are given along with an angle measurement opposite one of the two sides, the

triangle is an SSA triangle. We refer to this as the ambiguous case because depending on the

measurements, we may find one, two, or no possible triangle(s) with the given measurements. Some

texts utilize the Law of Sines to solve SSA triangles, providing tests that can be performed to determine

how many triangles there are before calculations are made, lengthening the solving process. Because the

maximum output for inverse sine is 90°, using this method often overlooks obtuse angles without

conducting the tests first.

If 𝑎, 𝑏, and 𝐴 are given, o If 𝐴 < 90° and

If 𝑎 > 𝑏, there is one acute triangle.

If 𝑎 < 𝑏 sin𝐴, there is no triangle.

If 𝑎 = 𝑏 sin𝐴, there is one right triangle.

If 𝑎 > 𝑏 sin𝐴, there is one acute triangle and one obtuse triangle.

o If 𝐴 > 90° and

If 𝑎 > 𝑏, there is one obtuse triangle.

If 𝑎 < 𝑏, there is no triangle.

Example 1 – In triangle 𝑋𝑌𝑍, 𝑥 = 50 cm, 𝑧 = 80 cm, and 𝑋 = 26°. Solve this/these triangle(s) using the

Law of Sines.

An alternate (and less time-consuming) method for solving an SSA triangle is by using the Law of Cosines.

No tests need to be used prior to calculations. The Law of Cosines combined with the Quadratic Formula

will yield one, two, or no solution(s) for the missing side length. If the result is two positive side lengths,

then there are two triangles, and both triangles will be solved separately. If the result is one positive side

length, then there is only one triangle needing to be solved, and the negative side length or duplicate side

length can be ignored. If there is no real solution, then there is no triangle matching the given

measurements.

Example 2 – In triangle 𝑋𝑌𝑍, 𝑥 = 50 cm, 𝑧 = 80 cm, and 𝑋 = 26°. Solve this/these triangle(s) using the

Law of Cosines.



Example 3 – Solve the triangle: 𝑎 = 3, 𝑏 = 2, 𝐴 = 40°.

Example 4 – Solve the triangle: 𝑎 = 6, 𝑏 = 8, 𝐴 = 35°.

Example 5 – Solve the triangle: 𝑎 = 2, 𝑐 = 1, 𝐶 = 50°.

Example 6 - A cow is tethered to one corner of a square barn, 10 feet by 10

feet, with a rope 100 feet long. What is the maximum grazing area for the

cow?




In exercises 1 – 12, solve for all possible triangles and find each area.

1. ∆𝐴𝐵𝐶: 𝐵 = 34°, 𝑎 = 4, 𝑏 = 3

2. ∆𝑋𝑌𝑍: 𝑋 = 13°, 𝑥 = 12, 𝑦 = 5

3. ∆𝐴𝐵𝐶: 𝐵 = 34°, 𝑎 = 4, 𝑏 = 5

4. ∆𝑋𝑌𝑍: 𝑋 = 13°, 𝑥 = 12, 𝑦 = 15

5. ∆𝐴𝐵𝐶: 𝐵 = 34°, 𝑎 = 4, 𝑏 = 2

6. ∆𝑋𝑌𝑍: 𝑋 = 13°, 𝑥 = 12, 𝑦 = 60

7. ∆𝑅𝑆𝑇: 𝑅 = 130°, 𝑟 = 20, 𝑡 = 16

8. ∆𝑂𝐵𝑇: 𝑂 = 170°, 𝑜 = 19, 𝑡 = 11

9. ∆𝐴𝐵𝐶: 𝐴 = 19°, 𝑎 = 25, 𝑐 = 30

10. ∆𝐻𝑆𝐶:𝐻 = 28°, ℎ = 50, 𝑐 = 20

11. ∆𝑋𝑌𝑍: 𝑋 = 58°, 𝑥 = 9.3, 𝑧 = 7.5

12. ∆𝐵𝐼𝐺: 𝐵 = 110°, 𝑏 = 1000, 𝑔 = 900

13. If the barn in Example 6 is rectangular, 10 feet by 20 feet, what is the maximum grazing area for

the cow?

14. Radio station KROK plans to broadcast rock music to people on the beach near Ocean City.

Measurements show that Ocean City is 20 mi from KROK, at an angle 50° north of west. KROK’s

broadcast range is 30 mi.

a. Using the law of cosines, how far along the beach to the east of Ocean City can people hear

KROK?

b. There are two answers to part (a). Show that both answers have meaning in the real world.

c. KROK plans to broadcast only in an angle between a line from the station through Ocean

City and a line from the station through the point on the beach farthest to the east of Ocean

City that people can hear the station. What is the measure of this angle?

15. In attempting to fly from city 𝑃 to city 𝑄, an aircraft followed a course that was 10° in error. After

flying a distance of 50 miles, the pilot corrected the course by turning and flying 70 miles farther.

If the constant speed of the aircraft was 250 miles per hour, how much time was lost due to the

error?

16. The famous Leaning Tower of Pisa was originally, 184.5 feet high. At a distance of 123 feet from

the base of the tower, the angle of elevation to the top of the tower is found to be 60°.

a. Find the acute angle the tower makes with the ground.

b. Find the altitude of the top of the tower to the ground.

Module 7 - Selected Solutions

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Pre-AP Precalculus Module 7 Triangle Applications