PROBLEM INVOLVING APPLICATIONS OF RIGHT TRIANGLES

SIMPLE PROBLEMS

1. At a certain time, the angle of elevation of the sun was 35º. How long was the shadow of the building, 1.5 m tall, at that time?

2. At a point 28 m away, the angle of elevation of a building is 65º. How tall is the building?

3. An 8-meter ladder is made to lean against a wall. The foot of the ladder is 6 m away from the base of the wall. Find the angle determined by the wall and the ladder.

4. Find the angle of elevation of the sun if the shadow of a 5-meter flagpole is 2 meters.

5. From the top of a cliff 126 meters high, the angle of depression of a boat is 20.7º. How far is the boat from the foot of the cliff?

NAVIGATION PROBLEMS

COURSE –angle measured in degrees, clockwise from the north to the direction in which the carrier is traveling. BEARING – angle measured in degrees, clockwise from the north from the observer to any location.KNOTS (nautical miles per hour) – unit of speed.

6. (Taken from Example # 6, of page 362) A navigator on a ship is sailing on a course of 338º at 12 knots observing a lighthouse, due north of the ship. Fifteen minutes later, the lighthouse is due east of the ship. How far is the lighthouse from the ship at that time?

7. (Taken from item no.43 of page 363) Two ships leave a port at the same time. The first ship on a course of 35º at 15 knots while the second ship sails on a course of 125º at 20 knots. Find, after two hours (a) the distance between the ships, (b) the bearing from the first ship to the second, and (c) the bearing from the second to the first.

PROBLEM INVOLVING TWO TRIANGLES

8. A student observes that the angle of elevation of the top of the tree is 5º. After walking 100 meters toward the tree, the angle of elevation is 15º. How tall is the tree?

HOMEWORK (1/4 sheet):

page 364, #44: A ship leaves a port and sails for 4 hours on a course of 78º at 18 knots. Then the ship changes its course to 168º and sails for 6 hours at 16 knots. After 10 hours, (a) what is the distance of the ship from the port and (b) what is the bearing from the port to the ship?

and page 380, #90: At a point P south of a building, the angle of elevation to the top of the building is 58º. At a point Q, 250 west of P, the angle of elevation is 27º. Find the height of the building.

Problems’ illustration are available at the book College Algebra and Trigonometry by Louis Leithold