Question

From the base of the tower, you walk 36.37 m.From there, you use the clinometer to measure the angleof incline from your eye to the top of the tower, and findthat it is 75º..You measure from the ground to your eye. The distance is1.63 m.How tall is the tower?Round to two decimal places if necessary

Answer 1

Let us begin by showing the problem on a diagram.

Let the height of the tower be x

Using trigonometric ratios, we can find the value of x

Let us label the sides of the resulting right-angled triangle:

Hence:

$\begin{gathered} \tan 75^0\text{ = }\frac{opposite}{adjacent} \\ \tan 75^0\text{ = }\frac{x-\text{ 1.63}}{36.37} \\ \text{Cross}-\text{Multiply} \\ x\text{ -1.63 = 135.735} \\ x\text{ = 135.735 + 1.63} \\ x\text{ = 137.365} \\ x\text{ }\approx\text{ 137.37m} \end{gathered}$

The height of the tower is 137.37m