Question

calculating unknown lengths of right triangles
the measure of angle a is 15°, and the length of side bc is 8. what are the lengths of the other two sides, rounded to the nearest tenth?
ac =
ab =

Explanation:

Step1: Identify trigonometric ratios

For $\angle A = 15^\circ$, $BC=8$ is opposite, $AC$ is adjacent, $AB$ is hypotenuse.

Step2: Calculate adjacent side $AC$

Use tangent: $\tan(15^\circ)=\frac{BC}{AC}$
$AC=\frac{BC}{\tan(15^\circ)}=\frac{8}{\tan(15^\circ)}$
$\tan(15^\circ)\approx0.2679$, so $AC\approx\frac{8}{0.2679}\approx29.9$

Step3: Calculate hypotenuse $AB$

Use sine: $\sin(15^\circ)=\frac{BC}{AB}$
$AB=\frac{BC}{\sin(15^\circ)}$
$\sin(15^\circ)\approx0.2588$, so $AB\approx\frac{8}{0.2588}\approx30.9$

Answer:

$AC \approx 29.9$
$AB \approx 30.9$