Chapter 8, Problem 17CR

(a)

To determine

To find: the tangent of a given angle

Answer to Problem 17CR

The tangent of the angle A is 1.5

Explanation of Solution

Given information:

A right triangle with a given measure of two sides.

Formula used:

In a right triangle the tangent of the angle is the ratio of the measure of side opposite to the angle to that adjacent to the angle.

  

It can be expressed as,

  $\tan B=\frac{a}{b}$

Calculation:

  

Based on the figure, tangent of the angle A can be expressed as,

  $\begin{array}{c}\tan A=\frac{9}{6}\\ =1.5\end{array}$

(b)

To determine

To find: the tangent of a given angle

Answer to Problem 17CR

The tangent of the angle B is 0.6667

Explanation of Solution

Given information:

A right triangle with a given measure of two sides .

Formula used:

In a right triangle the tangent of the angle is the ratio of the measure of side opposite to the angle to that adjacent to the angle.

  

It can be expressed as,

  $\tan B=\frac{a}{b}$

Calculation:

  

Based on the figure, tangent of the angle B can be expressed as,

  $\begin{array}{c}\tan B=\frac{6}{9}\\ =0.6667\end{array}$

(c)

To determine

To find: a given angle

Answer to Problem 17CR

The measure of angle B is 34⁰

Explanation of Solution

Given information:

A right triangle with a given measure of two sides.

Formula used:

In a right triangle the tangent of the angle is the ratio of the measure of side opposite to the angle to that adjacent to the angle.

  

It can be expressed as,

  $\tan B=\frac{a}{b}$

Therefore, angle B can be calculated by,

  $m\angle B={\tan }^{-1}\left(\frac{a}{b}\right)$

Calculation:

  

Based on the figure, angle B can be expressed as,

  $\begin{array}{c}m\angle B={\tan }^{-1}\left(\frac{6}{9}\right)\\ =33.69\\ \simeq 34°\end{array}$