Question

Solve triangle ABC using the given measurements if $b=6,C=90{}^{\circ }\text{and}c=13$. Round measure of sides to the nearest tenth and angles to nearest degree.

Short answer

The solution for triangle ABC is$a=11.5,A=62{}^{\circ }\text{and}B=28°$.

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 $b=6,C=90{}^{\circ }\text{and}c=13$.

Step 2. Calculation.

In triangle ABC, $b=6,C=90{}^{\circ }\text{and}c=13$.

Now, in right triangle ABC,

$\begin{array}{c}{c}^2=a^2+b^2\text{\hspace{0.17em}gives,}\\ {13}^2=a^2+6^2\\ a^2={13}^2-6^2\\ a=\sqrt{{13}^2-6^2}\\ a=11.5\end{array}$

Now by trigonometric ratios,

$\begin{array}{c}\cos B=\frac{a}{c}\\ \cos B=\frac{11.5}{13}\\ B={\cos }^{-1}\left(\frac{11.5}{13}\right)\\ B=28°\end{array}$

Now, $C=90{}^{\circ }\text{and}B=28°$, therefore by angle sum property $A=62°$.

Step 3. Conclusion.

Thesolution for triangle ABC, is $a=11.5,A=62{}^{\circ }\text{and}B=28°$.