Question

Solve triangle ABC using the given measurements if $b=7,C=90{}^{\circ }\text{and}c=18$. Round measure of sides to the nearest tenth and angles to nearest degree.

Short answer

The solution for triangle ABC is$a=16.6,A=67{}^{\circ }\text{and}B=23°$.

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 $b=7,C=90{}^{\circ }\text{and}c=18$.

Step 2. Calculation.

In triangle ABC, $b=7,C=90{}^{\circ }\text{and}c=18$.

Now, in right triangle ABC,

$\begin{array}{c}{c}^2=a^2+b^2\text{\hspace{0.17em}gives,}\\ {18}^2=a^2+7^2\\ a^2={18}^2-7^2\\ a=5\sqrt{11}\\ a=16.6\end{array}$

Now by trigonometric ratios,

$\begin{array}{c}\cos B=\frac{a}{c}\\ \cos B=\frac{16.6}{18}\\ B={\cos }^{-1}\left(\frac{16.6}{18}\right)\\ B=23°\end{array}$

Now, $C=90{}^{\circ }\text{and}B=23°$, therefore by angle sum property $A=67°$.

Step 3. Conclusion.

Thesolution for triangle ABC, is $a=16.6,A=67{}^{\circ }\text{and}B=23°$.