Chapter 8, Problem 19CR

(a)

To determine

To find: the cosine of a given angle

Answer to Problem 19CR

The cosine of the angle J is 0.9231

Explanation of Solution

Given information:

A right triangle with a given measure of three sides .

Formula used:

In a right triangle the cosine of the angle is the ratio of the measure of side adjacent to the angle to the hypotenuse.

  

It can be expressed as,

  $\cos B=\frac{b}{c}$

Calculation:

  

Based on the figure, cosine of the angle J can be expressed as,

  $\begin{array}{c}\cos J=\frac{24}{26}\\ =0.9231\end{array}$

(b)

To determine

To find: the sine of a given angle

Answer to Problem 19CR

The sine of the angle K is 0.9231

Explanation of Solution

Given information:

A right triangle with a given measure of three sides .

Formula used:

In a right triangle the sine of the angle is the ratio of the measure of side opposite to the angle to the hypotenuse.

  

It can be expressed as,

  $\sin B=\frac{a}{c}$

Calculation:

  

Based on the figure, sine of the angle K can be expressed as,

  $\begin{array}{c}\sin K=\frac{24}{26}\\ =0.9231\end{array}$

(c)

To determine

To find: a given angle

Answer to Problem 19CR

The angle K is 67⁰

Explanation of Solution

Given information:

A right triangle with a given measure of three sides .

Formula used:

In a right triangle the sine of the angle is the ratio of the measure of side opposite to the angle to the hypotenuse.

  

It can be expressed as,

  $\begin{array}{l}\sin B=\frac{a}{c}\\ B={\sin }^{-1}\left(\frac{a}{c}\right)\end{array}$

Calculation:

  

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

  $\begin{array}{c}K={\sin }^{-1}\left(\frac{24}{26}\right)\\ ={\sin }^{-1}\left(0.9231\right)\\ =67.38\\ \simeq 67°\end{array}$