Question

Dhaulagiri is the 7th highest mountain in the world. Ms. Fink is walking through

the Hidden Valley, preparing for an ascent of the mountain. She looks up to the
mountain and measures the angle of elevation to be 47.3° and she knows she is
at an altitude of 4900m. She hikes 1000m closer to the mountain with no
elevation change and notes the angle of elevation to be 58.5°. How high above
sea level is Dhaulagiri?

Answer 1

4833 m

Explanation:

Given that her angle of elevation at the first recording is 47.3 at an altitude of 4900 m

We use Pythagoras Theorem to get this done

We can say that the opposite of the angle is the altitude, while the hypotenuse of the triangle, is the distance between herself and the top

Using the sine angle rule, we have

Sine 47.3 = 4900 / h

h = 4900 / sin 47.3

h = 4900 / 0.7349

h = 6668 m

This means that she was 6668 m away from the top of the mountain

She then moves 1000 m closer to the mountain top, this means that our h = 6668 - 1000

Using the same sine angle rule, we have

Sine 58.5 = o / 5668

o = 5668 * sine 58.5

o = 5668 * 0.8526

o = 4833 m

She is 4833 m above the sea level