Chapter 4.8, Problem 38E

(a)

To determine

To Present:To draw a right triangle from the given information.

Explanation of Solution

Given information: Given height of the basketball backboard and the shadow cast by the backboard.

Let $\Delta \text{ABC}$ be the required triangle in which side AB represent the height of the basketball backboard, BC represent the shadow cast by the basketball backboard and angle of elevation be $\theta$

  

(b)

To determine

To Find:To find a trigonometric equation for the given information.

Answer to Problem 38E

The answer is $\mathrm{Tan}\theta =\frac{75}{104}$

Explanation of Solution

Given information:Given height of the basketball backboard and the shadow cast by the backboard.

In $\Delta \text{ABC}$ ,

  $\begin{array}{l}\text{AB}=12\frac{1}{2}\\ \text{BC}=17\frac{1}{3}\end{array}$

So,

  $\begin{array}{l}\mathrm{Tan}\theta =\frac{\text{AB}}{\text{BC}}\\ \mathrm{Tan}\theta =\frac{12\frac{1}{2}}{17\frac{1}{3}}\\ \mathrm{Tan}\theta =\frac{\frac{25}{2}}{\frac{52}{3}}\\ \mathrm{Tan}\theta =\frac{75}{104}\end{array}$

Hence, the required equation is $\mathrm{Tan}\theta =\frac{75}{104}$

(c)

To determine

To Find:To find the angle of elevation of the sun.

Answer to Problem 38E

The angle is $35.8°.$

Explanation of Solution

Given information:Given equation is $\mathrm{Tan}\theta =\frac{75}{104}$

Since the given equation is

  $\begin{array}{l}\mathrm{Tan}\theta =\frac{75}{104}\\ \mathrm{Tan}\theta =\mathrm{Tan}(35.8°)\\ \therefore \theta =35.8°\end{array}$

Hence, the required angle is $35.8°.$