Chapter 12.5, Problem 1WE

To determine

Solve the right triangle ABC for which $\angle A=36.2°\text{ and }c=68$ . Give the length to three significant digits and angle measures to nearest ten minutes.

  

Answer to Problem 1WE

The three sides of triangle are $a=40.2,b=54.9\text{ and }c=68.0$ . And three angles are $\angle A=36.2°,\angle B=53.8°\text{ and }\angle C=90°$ .

Explanation of Solution

Given information: The given triangle ABC has $\angle A=36.2°\text{ and }c=68$ .

  

Calculation: Since the triangle ABC has $\angle A=36.2°\text{ and }c=68$ . And it is right angle at point $\left(C\right)$ .

  $\begin{array}{c}\angle B=90-36.2°\mathrm{....}\left(\because \angle C=90\right)\\ =53.8°\end{array}$

Now by trigonometric ratios,

  $\begin{array}{c}\sin A=\frac{a}{c}\\ \sin \left(36.2°\right)=\frac{a}{68}\\ \text{or, }a=68\sin \left(36.2°\right)\\ a=40.2\end{array}$

Similarly,

  $\begin{array}{c}\cos A=\frac{b}{c}\\ \cos \left(36.2°\right)=\frac{b}{68}\\ \text{or, }b=68\cos \left(36.2°\right)\\ b=54.9\end{array}$

Hence the given triangle ABC has sides $a=40.2,b=54.9\text{ and }c=68.0$ . And three angles $\angle A=36.2°,\angle B=53.8°\text{ and }\angle C=90°$ .