Chapter 8, Problem 32RE

Finding the Height of a Helicopter Two observers simultaneously measure the angle of elevation of a helicopter. One angle is measured as $25°$, the other as $40°$ (see the figure). If the observers are 100 feet apart and the helicopter lies over the line joining them, how high is the helicopter?

To determine

To find: How high is the helicopter?

Answer to Problem 32RE

The helicopter is about $\text{29}\text{.97}$ feet high.

Explanation of Solution

Given:

Two observers simultaneously measure the angle of elevation of a helicopter. One angle is measured as $25°$, the other as $40°$ (see the figure). The observers are 100 feet apart and the helicopter lies over the line joining them.

Formula used:

$\frac{\text{sinA}}{\text{a}}=\frac{\text{sinB}}{\text{b}}=\frac{\text{sinC}}{\text{c}}$

$\text{sinθ }=\text{ opp}/\text{hyp}$

Calculation:

Let $h$ be the height of the helicopter.

Let $x$ be the distance from the observer to the helicopter and $\text{θ}$ be $\angle ACB$.

$\theta =180°-40°-25°=115°$

$\theta =115°$

$\frac{\text{sin}40°}{x}=\frac{\text{sin}115°}{100}$

$x=100\frac{\text{sin}40°}{\text{sin}115°}$

$x=70.92$

$x=70.92\text{ ft}$

$\sin 25=h/70.92$

$h=70.92*\text{ sin}25$

$h=29.97$

$h=29.97\text{ ft}$

The helicopter is about $29.97$ feet.