Chapter 8.2, Problem 54AYU

To determine

To find: The height of the aircraft.

Answer to Problem 54AYU

The height of the aircraftis $710.45\text{ft}$ .

Explanation of Solution

Given information:

The displace between the sensors is $700\text{ft}$ , the angle of elevation from the first sensor to the aircraft is $20°$ , and from the second sensor to the aircraft is $15°$ .

Consider the following figure,

  

From the figure, calculate thebaseAD from the triangle ABD,

  $\begin{array}{l}\tan \left(20°\right)=\frac{AB}{AD}\\ \tan \left(20°\right)=\frac{h}{x}\\ x=2.747h\end{array}$

The height of the aircraftis calculated as from triangle ABC,

  $\begin{array}{l}\text{tan15}°=\frac{h}{x+700}\\ \text{tan15}°=\frac{h}{2.747h+700}\\ 0.736h+187.56=h\\ h=710.45\text{ft}\end{array}$

Therefore, the height of the aircraft is $710.45\text{ft}$ .