Trigonometry Supplemental Questions

Problem 1 Jessica observed a mountain climber reaching the summit, which is known to be at 2,358 ft. If Jessica is standing 1500 ft. from the base, at what angle did she sight the mountain climber to the nearest degree?

What’s your strategy? 1.Draw a figure to represent the problem. 2.Determine which trigonometric ratio to use. 3.Calculate the angle of elevation.

1. Draw a figure to represent the problem. 2,358 ft. 1,500 ft. x° M S C

2. Determine which trigonometric ratio to use. 2,358 ft. 1,500 ft. x° Opposite Adjacent Tangent M S C

3. Calculate the Angle of Elevation. Tan C° = MS SC Tan x° = 2,358 ft. 1,500 ft. x = Tan -1 2,358 ft. 1,500 ft. x = ° C≈ 58° ∨

Problem 2 A rescue helicopter pilot sights a life raft at a 26 o angle of depression. The helicopter is 3 km above the water. What is the pilot’s distance from the raft on the surface of the water to the nearest km?

What’s your strategy? 1.Draw a figure to represent the problem. 2.Determine which trigonometric ratio to use. 3.Calculate the surface distance.

1. Draw a figure to represent the problem. 3 km x km H W R 26° Alternate Interior Angles

2. Determine which trigonometric ratio to use. 3 km x km H W R 26° Opposite Adjacent Tangent

3. Calculate the surface distance. Tan R° = HW WR Tan 26° = 3 km x km x (Tan 26°) = 3 km x = 3 km Tan 26° x = WR ≈ km

Kevin is standing at the back of the cruise ship and observes two sea turtles following each other, swimming in a straight line in the opposite direction of the ship. Kevin’s position is 206 meters above sea level and the angles of depression to the two sea turtles are 43° and 47°. Calculate the distance between the two sea turtles to the nearest meter. K 206 m 47° 43° S TO Problem 3

What’s your strategy? 1.Separate and re-draw the two triangles. 2.Calculate individual horizontal distances. 3.Calculate the difference between the two horizontal distances.

K 206m 47° 43° S T O x 206m O y 47° 43° K 1. Separate and re-draw the two triangles.

2. Calculate individual horizontal distances. Tan S° = KO SO Tan 43° = 206 m x x (Tan 43°) = 206 m x = 206 m Tan 43° x = SO = m Tan T° = KO TO Tan 47° = 206 m y x (Tan 47°) = 206 m x = 206 m Tan 47° x = TO = m

3. Calculate the differences between the two horizontal distances. ST = SO – TO ST = – ST = ST ≈ 28 m