- 81 - Law of Sines/Law of Cosines worksheet Set up and label a diagram. Then show the equation(s) you can use to solve the problem. Finally, solve it! Give your answers with lengths rounded to 4 significant digits, angles in degree/minute/second form rounded to whole numbers. 1. To find the distance AB across a river, a distance BC = 354 m is measured off on one side of the river.

It is found that m∠ABC = 112o 10' and m∠BCA = 15o 20'. Find AB. 2. The sides of a parallelogram are 4.0 cm and 6.0 cm. One angle is 58o while another is 122o. Find the

lengths of the diagonals of the parallelogram. 3. From points P and Q, 180 meters apart on an east-west line, a tree is sighted on the opposite side of a

deep ravine. From point P, a compass indicates that the bearing of the tree is 27o. From Q, the bearing of the tree is 43o. How far from P is the tree? (Note: pay attention to what order P and Q must be in)

- 82 - 4. To determine the distance RS across a deep canyon, Joanna measures a distance TR = 582 yd. She then

finds that m∠ STR = 32o 50' and m∠ SRT = 102o 20'. Find RS. 5. A baseball diamond is a square, 90 ft on a side, with home plate and the three bases as vertices. The

pitcher's rubber is located 60.5 ft from home plate on a direct line from home to 2nd. Find the distance from the pitcher's rubber to each of the bases.

6. The Vietnam Veterans' Memorial in Washington, D.C., is in the shape of an unenclosed isosceles

triangle (that is, V-shaped) with equal sides of length 246.75 feet and the angle between these sides measuring 125o 12'. Find the distance between the ends of the two equal sides.

- 83 - 7. A parallelogram has a side of length 40 and a diagonal of length of 75. If the angle between these

two is 37o, find the length of the other side of the parallelogram. 8. A ship is sailing due north. At a certain point the bearing of a lighthouse 12.5 km away is N 38.8o E.

Later on, the captain notices that the bearing of the lighthouse has become S 44.2o E. How far did the ship travel between the two observations of the lighthouse?

9. Two airplanes have elevations of 23,000 feet and 18,000 feet. Both are flying east toward an airport

control tower. The plane with the higher elevation is closer to the airport than the second plane. From the control tower, the angle of elevation of the plane closest to the airport is 4o and the angle of elevation of the second plane is 2.5o. How many miles apart are the planes? (5280 feet = 1 mile)

- 84 - 10. The bearing of a lighthouse from a ship was found to be N 37o E. After the ship sailed 2.5 miles due

south, the new bearing was N 25o E. Find the distance between the ship and the lighthouse at each location.

11. Two boats leave a dock together. Each travels in a straight line. The angle between their courses

measures 54o 10'. One boat travels 36.2 km per hr, and the other travels 45.6 km per hr. How far apart will they be after 3 hours?

12. A property is described as follows: From a granite post, proceed 195 feet east along Hill Road, then

turn and head along a bearing of S 32o E for 260 feet. Then head directly back to the granite post. What is the area, in square feet, of this property?

- 85 - 13. A sailboat leaves its dock and proceeds due east for 2 miles. It then changes course to 205o and

travels until it is due south of the dock. How far south of the dock is the sailboat? 14. A hill makes an angle of 14.3o with the horizontal. From the base of the hill, the angle of elevation to

the top of a tree on top of the hill is 27.2o. The distance along the hill from the base to the tree is 212 ft. Find the height of the tree.

15. Two hikers are following a trail that separates into two forks. Each hiker takes a different fork. The

forks diverge at an angle of 67o. If the first hiker walks at a speed of 3.5 mph and the second hiker walks at a speed of 2 mph, how far apart are the hikers after 2 hours?

- 86 - 16. Sam first walks 6 miles due north, then 2 miles at N 70o E. How far is he from his starting point? 17. A pilot travels to a city by going due north at 325 mph for 30 minutes, then turning and going N 40o W at 300 mph for 45 minutes. If he were to fly directly there instead, what bearing should he

use? 18. In the problem above, if he is to fly directly there at a speed of 350 mph, how long would the trip

take?

- 87 - 19. A surveyor sights a tree directly across a river and then measures 80 feet along the bank. At the new

location, she finds that the angle between the riverbank and her line of sight to the tree is 42o. How wide is the river?

20. A balloonist is directly above a straight road 1.5 mi. long that joins two villages. She finds that the

town closer to her is at an angle of depression of 35o and the further town is at an angle of depression of 31o. How high above the ground is the balloon?