Question

ating 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: Define trigonometric ratios

For $\angle A = 15^\circ$, $\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AC}$, $\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{BC}{AB}$

Step2: Solve for adjacent side AC

Rearrange $\tan(A)$ to solve for $AC$:
$AC = \frac{BC}{\tan(15^\circ)}$
Substitute $BC=8$, $\tan(15^\circ)\approx0.2679$:
$AC = \frac{8}{0.2679} \approx 29.9$

Step3: Solve for hypotenuse AB

Rearrange $\sin(A)$ to solve for $AB$:
$AB = \frac{BC}{\sin(15^\circ)}$
Substitute $BC=8$, $\sin(15^\circ)\approx0.2588$:
$AB = \frac{8}{0.2588} \approx 30.9$

Answer:

$AC = 29.9$
$AB = 30.9$