Question

The angle of elevation from a point on the ground to the top of a tower is 36° 30'. The angle of elevation from a point 140 feet farther back from the tower is 25° 51'. Find the height of the tower. Round your answer to the hundredths place.

Answer 1

67.83 feet

Explanation:

Let h be the height of the tower and d be the distance from the point on the ground to the tower at an angle of elevation of 25° 51' from the tower. The line of sight of this point from the top of the tower, h and d form a right-angled triangle with the line of sight at an angle of elevation of 25° 51' being the hypotenuse side.

Using trigonometric ratios,

tan25° 51' = h/d

h = dtan25° 51'

We convert to degrees 25° 51'

25° 51' = 25° + 51' × 1°/60' = 25° + 0.85° = 25.85°

So, h = dtan25.85°

d = 140 feet

h = 140tan25.85°

h = 140 × 0.4845

h = 67.83 feet