Question

From the base of the tower, you walk 36.37 m. From there, you use the clinometer to measure the angle of incline from your eye to the top of the tower, and find that it is 75°. You measure from the ground to your eye. The distance is 1.63 m. How tall is the tower? (Round to two decimal places if necessary)

Answer 1

ANSWER

137.37 m

EXPLANATION

Let's draw a diagram of this situation first,

As we can see, there is a right triangle formed by the tower and your eye level. We know that the distance between the ground and your eye is 1.63m, so the height of the tower is,

$h=d+1.63m$

Using trigonometric ratios we can find the vertical distance from your eye to the top of the tower, d. We know the angle from your eye to the top of the tower, the distance between you and the base of the tower (which is the adjacent side of the angle) and we want to find the opposite side to the given angle. We use the tangent of the angle,

$\tan 75=\frac{d}{36.37m}$

Solving for d,

$d=36.37m\cdot\tan 75\approx135.74m$

Hence, the height of the tower is,

$h=1.63m+135.74m=137.37m$