Chapter 9.5, Problem 48E

To determine

To find: theheight of the cliff.

Answer to Problem 48E

The height of the cliff is $210.48\text{ft}\text{.}$

Explanation of Solution

Given information:

The elevation angle from a point is ${60}^{\circ }$ and from the point $45$ feet farther away the angle of elevation to the top of the cliff is ${52}^{\circ }$ .

Calculation: to find the height of the cliff, let $y$ is the height of the cliff,

  $\begin{array}{l}\tan {52}^{\circ }=\frac{y}{x+45}\\ \tan {60}^{\circ }=\frac{y}{x}\\ \frac{\tan {52}^{\circ }}{\tan {60}^{\circ }}=\frac{x}{x+45}\text{ [divide both eq}\text{.]}\\ \frac{1.27}{1.732}=\frac{x}{x+45}\text{ [substitute the values]}\\ 0.73\left(x+45\right)=x\text{ [divide and multiply]}\\ \text{0}\text{.27}x=\text{32}\text{.85 [multiply and subtract]}\\ x=121.67\text{ [divide]}\\ 1.73=\frac{y}{121.67}\text{ [substitute]}\\ y=210.48\text{ft}\text{. [multiply]}\end{array}$

Thus, The height of the cliff is $210.48\text{ft}\text{.}$