Question

Explain how you would measure the height of a TV tower that is on the roof of a tall building.

Short answer

By using the trigonometric function $\tan \theta$, we can arrive at an function with the height $h=x.\tan \theta -y$

Step-by-step solution

Step 1. Given Information

The TV tower is on the roof of the building.

Step 2. Construction of TV tower on the building.

Let $BC$be the height of the building and $CD$be the height of the TV tower on the building.

Let Abe the point which is xfeet away from the building so that $AB=x$.

Let the measure of an angle from A to C be $\alpha$ and the measure of angle from A to TV tower is $\theta$

Step 3. Find y

By using tangent function on the triangle $ABC$,

$$\begin{gathered} \tan \alpha =\frac{y}{x} \\ y=\tan \alpha \end{gathered}$$

Step 4. Find h

Now consider the triangle ABD,

$$\begin{gathered} \tan \theta =\frac{h+y}{x} \\ h+y=x\tan \theta \\ h=x\tan \theta -y \end{gathered}$$

which the height of the tower.