Chapter 8, Problem 20CR

(a)

To determine

To find: the measure of the side WX of the given triangle WVX

Answer to Problem 20CR

The measure of side WX is 117 units

Explanation of Solution

Given information:

A right triangle with a given measure of other angles and one side .

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, the relation between the hypotenuse WX and the altitude can be expressed as,

  $\begin{array}{l}\sin 40°=\frac{75}{WX}\\ WX=\frac{75}{\sin 40°}\end{array}$

Now, with the use of the table of trigonometric values in Page 311 in the textbook,

  $\begin{array}{c}WX=\frac{75}{0.6428}\\ =116.67\\ \simeq 117\end{array}$

(b)

To determine

To find: the measure of the side VX of the given triangle WVX

Answer to Problem 20CR

The measure of side VX is 90 units

Explanation of Solution

Given information:

A right triangle with a given measure of other angles and one side

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, the relation between the hypotenuse WX and VX (marked as x) can be expressed as,

  $\begin{array}{l}\sin 50°=\frac{x}{WX}\\ x=WX\sin 50°\end{array}$

Now, substituting the value of hypotenuse and with the use of the table of trigonometric values in Page 311 in the textbook,

  $\begin{array}{c}x=117\times 0.7660\\ =89.62\\ \simeq 90\end{array}$