Question

find the value of each variable using sine and cosine. round your answers to the nearest tenth.
a right-angled triangle, hypotenuse labeled n, sides adjacent to right angle are labeled m and 8, angle between side labeled m and hypotenuse is labeled 50 degrees.
$m \approx \square$
$n \approx \square$

Explanation:

Step1: Relate m to 50° via cosine

$\cos(50^\circ) = \frac{m}{n}$

Step2: Relate 8 to 50° via sine

$\sin(50^\circ) = \frac{8}{n}$

Step3: Solve for n first

Rearrange sine formula: $n = \frac{8}{\sin(50^\circ)}$
Calculate: $n \approx \frac{8}{0.7660} \approx 10.4$

Step4: Solve for m using cosine

Rearrange cosine formula: $m = n \cos(50^\circ)$
Substitute $n \approx 10.4$: $m \approx 10.4 \times 0.6428 \approx 6.7$

Answer:

$m \approx 6.7$
$n \approx 10.4$