Question

Solve triangle ABC using the given measurements if $B=27{}^{\circ },C=90{}^{\circ }\text{and}b=7$. Round measure of sides to the nearest tenth and angles to nearest degree.

Short answer

The solution for triangle ABC is$a=13.7,c=15.4\text{and}\angle A=63°$.

Step-by-step solution

Step 1. Write down the given parameters of triangle.

The given triangle ABC is shown below whose parameters are represented as $B=27{}^{\circ },C=90{}^{\circ }\text{and}b=7$.

Step 2. Calculation.

In triangle ABC, $B=27{}^{\circ },C=90{}^{\circ }\text{and}b=7$. Therefore, $\angle A=63°$ by angle sum property.

Now, trigonometric ratios,

$\begin{array}{c}\sin B=\frac{b}{c}\\ \sin 27°=\frac{7}{c}\\ c=7\csc \left(27°\right)\\ c=15.4\end{array}$

Now, in right triangle ABC by Pythagoras Theorem.

$\begin{array}{c}{c}^2=a^2+b^2\text{\hspace{0.17em}gives,}\\ {15.4}^2=a^2+7^2\\ a^2={15.4}^2-7^2\\ a=\sqrt{{15.4}^2-7^2}\\ a=13.7\end{array}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a=13.7,c=15.4\text{and}\angle A=63°$.