Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Calculate angle S

The sum of angles in a triangle is $180^\circ$.
$\angle S = 180^\circ - 35^\circ - 99^\circ = 46^\circ$

Step2: Find side s via Law of Sines

Relate side s, angle S, side SU, angle T.
$\frac{s}{\sin(46^\circ)} = \frac{12}{\sin(99^\circ)}$
$s = \frac{12 \times \sin(46^\circ)}{\sin(99^\circ)}$
$s \approx \frac{12 \times 0.7193}{0.9877} \approx 8.7$

Step3: Find side u via Law of Sines

Relate side u, angle U, side SU, angle T.
$\frac{u}{\sin(35^\circ)} = \frac{12}{\sin(99^\circ)}$
$u = \frac{12 \times \sin(35^\circ)}{\sin(99^\circ)}$
$u \approx \frac{12 \times 0.5736}{0.9877} \approx 6.9$

Answer:

$\angle S = 46^\circ$, $s \approx 8.7$, $u \approx 6.9$