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Expert-verified Found in: Page 707 ### Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903 # Solve triangle ABC using the given measurements if $B=15{}^{\circ },C=90{}^{\circ }\text{and}\phantom{\rule{-0.2em}{0ex}}\text{}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\text{}c=25$. Round measure of sides to the nearest tenth and measures of angles to nearest degree.

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

See the 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 $B=15{}^{\circ },C=90{}^{\circ }\text{and}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\text{}c=25$. ## Step 2. Calculation.

In triangle ABC, $B=15{}^{\circ },C=90{}^{\circ }\text{and}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\text{}c=25$. Therefore, $\angle A=75°$ by angle sum property.

Now, trigonometric ratios,

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

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.

The solution for triangle ABC, is $a=24.1,b=6.5\text{and}A=75°$. ### Want to see more solutions like these? 