Question

To find the height of a mountain, surveyors often find the angle of elevation to the top from two points at the same altitude a fixed distance apart. Suppose that the angles of the elevation from two points 500 meters apart are 35.333333333 degrees and 25.766666666666 degrees. How high is the mountain above the altitude of the two points

Answer 1

Answer:the height if the mountain is 143.59 feet

Explanation:

The diagram representing the situation is shown in the attached photo.

h represents the height of the mountain.

We would apply trigonometric ratio

Looking at triangle CAD,

Tan 35.33 = h/x

h = xtan 35.33 = x × 0.7088 = 0.7088x meters

Looking at triangle CBD,

Tan 25.77 = h/500 - x

h = 0.4828(500 - x)

h = 241.4 - 0.4828x

Therefore .

0.7088x = 241.4 - 0.4828x

0.7088x + 0.4828x = 241.4

1.1916x = 241.4

x = 241.4/1.1916 = 202.58

h = 0.7088x = 0.7088 × 202.58 = 143.59 feet