Question

Solve triangle ABC using the given measurements if $B=30{}^{\circ },C=90{}^{\circ }\text{and}b=11$. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short answer

The solution for triangleABC is$a=19.1,c=22\text{and}\angle A=60°$.

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 $B=30{}^{\circ },C=90{}^{\circ }\text{and}b=11$.

Step 2. Calculation.

In triangle ABC, $B=30{}^{\circ },C=90{}^{\circ }\text{and}b=11$. Therefore, $\angle A=60°$ by angle sum property.

Now, trigonometric ratios,

$\begin{array}{c}\sin B=\frac{b}{c}\\ \sin 30°=\frac{11}{c}\\ c=11\csc \left(30°\right)\\ c=22\end{array}$

Now, in right triangle ABC by Pythagoras Theorem.

$\begin{array}{c}{c}^2=a^2+b^2\text{\hspace{0.17em}gives,}\\ {22}^2=a^2+{11}^2\\ a^2={22}^2-{11}^2\\ a=\sqrt{{22}^2-{11}^2}\\ a=19.1\end{array}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a=19.1,c=22\text{and}\angle A=60°$.