Question

Solve triangle ABC using the given measurements if $B=15{}^{\circ },C=90{}^{\circ }\text{and}c=25$. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

Short answer

The solution for triangle ABC is $a=24.1,b=6.5\text{and}A=75°$.

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 $B=15{}^{\circ },C=90{}^{\circ }\text{and}c=25$.

Step 2. Calculation.

In triangle ABC, $B=15{}^{\circ },C=90{}^{\circ }\text{and}c=25$. Therefore, $\angle A=75°$ by angle sum property.

Now, trigonometric ratios,

$\begin{array}{c}\sin B=\frac{b}{c}\\ \sin 15°=\frac{b}{25}\\ b=25\sin \left(15°\right)\\ b=6.5\end{array}$

Now, in right triangle ABC,

$\begin{array}{c}{c}^2=a^2+b^2\text{\hspace{0.17em}gives,}\\ {25}^2=a^2+{6.5}^2\\ a^2={25}^2-{6.5}^2\\ a=\sqrt{{25}^2-{6.5}^2}\\ a=24.1\end{array}$

Step 3. Conclusion.

Thesolution for triangle ABC, is $a=24.1,b=6.5\text{and}A=75°$.