Trigonometry Answers

Two Olympic ski runs are compared. One has a vertical drop of 450 m for a horizontal run of 1.2 km, and the other a drop of 625 m for a run of 1.8 km. Which hill has the greater slope?

The grade of a road is 3%.

a) Calculate the vertical climb, in meters, for a horizontal distance of 1.5 km.

b) Calculate the run, in kilometers, necessary to reach the top of an 81 m high hill.

A surveyor has been given the job of finding the width of a river. She cannot measure the distance across the water, but she is able to obtain some measurements on land as shown in the diagram below. Based on her measurements, what is the width of the river?

From a position on the beach, Amelia can see two buoys that mark the turning points for a canoe race. The first buoy is in the lake 500 m straight ahead of Amelia. The angle from the first buoy, to Amelia, to the second buoy is 67°. If the buoys are 700 m apart, what is the angle from the first buoy to the second buoy to Amelia?

Find the course and distance from a position 37⁰ 01’ N 9⁰ 00’W to a position 36⁰ 11’N
6⁰ 02’W.

Marion needs to find the cosine of Pi over 12. If she knows that cos Pi over 6 = root 3 over 2, how can she use this fact to find the cosine of Pi over 12? What is her answer. Please explain and show your work

Determine the values of sin(2a), cos(2a) and tan(2a) , given cos(a) = -4/5 and Pi over 2 ≤ 0 ≤ Pi

Determine the values of sin(2a) and tan(2a), given tan(a) = -7/24 and Pi over 2 ≤ 0 ≤ Pi

Use a double angle formula to rewrite each trigonometric ratio

a) sin (4a)
b) cos (6a)
c) tan (5a)