Chapter 4.8, Problem 36E

a.

To determine

To find: The angle of evaluation of the sun.

Answer to Problem 36E

Draw a right angle triangle $\text{ABC}$ that given a visual representation of the problem.

Explanation of Solution

Given information: Height $=12\frac{1}{2}\text{ ft}.$ and shadow $17\frac{1}{3}\text{ ft}.$ long

Calculation:

  

Draw a right angle triangle $\text{ABC}$ that given a visual representation of the problem.

b.

To determine

To find: The angle of evaluation of the sun.

Answer to Problem 36E

  $\text{AC}$ is the basketball backboard’s height and $\text{AB}$ is it shadow.

Explanation of Solution

Given information: Height $=12\frac{1}{2}\text{ ft}.$ and shadow $17\frac{1}{3}\text{ ft}.$ long

Calculation:

  

  $AC$ is the basketball backboard’s height and $AB$ is it shadow.

c.

To determine

To find: The angle of evaluation of the sun.

Answer to Problem 36E

  $\therefore \theta \simeq {35.8}^{\circ }$

Explanation of Solution

Given information: Height $=12\frac{1}{2}\text{ ft}.$ and shadow $17\frac{1}{3}\text{ ft}.$ long

Calculation:

  

  $\begin{array}{l}\tan \theta =\frac{\text{AC}}{\text{AB}}\\ \Rightarrow \tan \theta =\frac{12.5}{17.333}\\ \Rightarrow \theta ={\tan }^{-1}\left(\frac{12.5}{17.333}\right)\\ \Rightarrow \theta \simeq {35.8}^{\circ }\end{array}$