Suggested languages for you:

Americas

Europe

Q32.

Expert-verifiedFound in: Page 707

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 $a=24.1,b=6.5\text{and}A=75\xb0$**.**

The given triangle ABC is shown below whose parameters are represented as $B=15{}^{\circ},C=90{}^{\circ}\text{and}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\phantom{\rule{-0.2em}{0ex}}\text{}c=25$.

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, $\angle A=75\xb0$ by angle sum property.

Now, trigonometric ratios,

$\begin{array}{c}\mathrm{sin}B=\frac{b}{c}\\ \mathrm{sin}15\xb0=\frac{b}{25}\\ b=25\mathrm{sin}\left(15\xb0\right)\\ b=6.5\end{array}$

Now, in right triangle ABC,

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

The** **solution for triangle *ABC*, is $a=24.1,b=6.5\text{and}A=75\xb0$.

94% of StudySmarter users get better grades.

Sign up for free