⦁ A mountaineer uses a clinometer to sight the top of a mountain at an angle of 70°. She walks 300 m closer to the mountain and now sights the top at an angle of 75°. How high is the mountain?

Answer 1

Draw and label a diagram!

h represents the height of the mountain

d represents the distance from the second position to the base of the mountain

tan 70° = h / (300 + d)

tan 70° (300 + d) = h

tan 75° = h / d

d tan 75° = h

tan 70°° (300 + d) = d tan 75°

Solve for d then solve for h.