Chapter 6, Problem 1RE

For Exercises 1-4, solve the right triangle for the unknown sides and angles. Round values to $1$ decimal place if necessary.

$B=37°,a=17$

To determine

To calculate: The unknown sides and angles for the provided right triangle if angle $B=37°$ and side $a=17$ .

Answer to Problem 1RE

The unknown sides of the right triangle are $b\approx 12.8\text{ and }c\approx 21.3$ and the unknown angle is $A=53°$ .

Explanation of Solution

Calculation:

Assume that the unknown sides of the right triangle are $b$ and $c$ .

Assume the unknown angle is $A$ (in degrees). It is given that angle $C=90°$ , $B=37°$ and one side $a=17$ .

The sum of all the angles of a triangle is $180°$ .

$\begin{array}{c}A+B+C=180°\\ A=180°-B-C\\ A=180°-37°-90°\\ A=53°\end{array}$

Find the side $b$ using the formula $\tan \theta =\frac{\text{Perpendicular}}{\text{Base}}$

$\begin{array}{c}\tan B=\frac{b}{a}\\ \tan 37°=\frac{b}{17}\\ b=\tan 37°\times 17\\ b\approx 12.8\end{array}$

Similarly,

$\begin{array}{c}\sin B=\frac{b}{c}\\ \sin 37°=\frac{12.8}{c}\\ c=\frac{12.8}{\sin 37°}\\ \approx 21.3\end{array}$

Hence, the unknown sides of the right triangle are $b\approx 12.8\text{ and }c\approx 21.3$ and the unknown angle is $A=53°$ .