Chapter 8.5, Problem 29STP

To determine

To calculate:

The height of cloud ceiling

Answer to Problem 29STP

The height of cloud ceiling is $6500ft$

Explanation of Solution

Given information:

The base length: $6500ft$

Angle of elevation: $45°$

Calculation:

Consider,

The height of cloud ceiling: $x$

The horizontal distance is $6500ft$ , and the angle of elevation is $45°$ .

Let’s draw a figure to represent the given information:

  

If is a $△ABC$ right triangle with acute $\angle A$ , then the tangent of $\angle A$ is the ratio of the length of

leg opposite $\angle A$ to the length of the leg adjacent $\angle A$ .

As per the definition of tangent, the height of cloud ceiling is calculated as:

  $\begin{array}{l}\tan 45°=\frac{x}{6500}\\ 6500\tan 45°=x\\ x\approx 6500ft\end{array}$

So, height of cloud ceiling is calculated as $x=6500ft$ .