Chapter 12.5, Problem 4WE

To determine

Solve the right triangle ABC for which $\angle A=82.1°\text{ and }b=246$ . Give the length to three significant digits and angle measures to nearest ten minutes.

  

Answer to Problem 4WE

The three sides of triangle are $a=1770,b=246\text{ and }c=1790$ . And three angles are $\angle A=82.1°,\angle B=7.9°\text{ and }\angle C=90°$ .

Explanation of Solution

Given information: The given triangle ABC has $\angle A=82.1°\text{ and }b=246$ .

  

Calculation: Since the triangle ABC has $\angle A=82.1°\text{ and }b=246$ . And it is right angle at point $\left(C\right)$ .

  $\begin{array}{c}\angle B=90°-82.1°\mathrm{....}\left(\because \angle C=90°\right)\\ =7.9°\end{array}$

Now by trigonometric ratios,

  $\begin{array}{c}\tan A=\frac{a}{b}\\ \tan \left(82.1°\right)=\frac{a}{246}\\ \text{or, }a=\left(246\right)\tan \left(82.1°\right)\\ a=1770\end{array}$

Similarly,

  $\begin{array}{c}\cos A=\frac{b}{c}\\ \cos \left(82.1°\right)=\frac{246}{c}\\ \text{or, }c=\frac{246}{\cos \left(82.1°\right)}\\ c=1790\end{array}$

Hence the given triangle ABC has sides $a=1770,b=246\text{ and }c=1790$ . And three angles $\angle A=82.1°,\angle B=7.9°\text{ and }\angle C=90°$ .