Question

You are about to run up a set of 100 stairs. The diagonal distance up the 100 stairs is 62.5

feet and the angle of elevation from the base of the stairs to the top is
31
62.5 ft.
h
31°
What is the height difference from where you start to where you finish?
Round your answer to the nearest hundredth.
h=
feet

Answer 1

h = 32.2 ft

Explanation:

Since we have a right triangle, to get the value of h, we will have to use the appropriate trigonometric ratio

From the diagram given, h faces the angle and that makes it the opposite side

62.5 ft faces the right angle and that makes it the hypotenuse

The trigonometric ratio that connects the two is the sine

thus, we have it that;

sine 31 = h/62.5

h = 62.5 * sin 31

h = 32.2 ft