Chapter 8.1, Problem 82AYU

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

To determine

To explain: How you would measure the height of a TV tower that is on the roof of a tall building.

Answer to Problem 82AYU

$\text{height of the tower }=x\tan \theta -x\tan \varphi$

Explanation of Solution

Given:

TV tower is on the roof of a tall building.

Formula used:

$\tan \theta =\frac{\text{opposite side}}{\text{Adjacent side}}$

Calculation:

Take a straw and a protractor.

Stand at a point and view the tip of the top of tower through the straw and measure the angle between straw and base on the ground.

Let the angle measured be $\theta$.

Stand at a point and view the tip of the foot tower through the straw and measure the angle between straw and base on the ground.

Let the angle measured be $\varphi$.

Measure the length from foot of the tower to the point where you stood and let it be $x$ ft.

$\tan \theta =\frac{\text{opposite side}}{\text{Adjacent side}}$

$\tan \theta \text{ = }\frac{\text{Height of the tower }+\text{ height of the building}}{x}$

$\text{tan}\varphi =\frac{\text{height of the building}}{x}$

Therefore $\text{height of the tower }=x\tan \theta -x\tan \varphi$.