Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.
(image of triangle with angles at t: 66°, at v: 77°, side opposite t is f, side opposite v is v, side opposite u is 8)

Explanation:

Step1: Find angle U

The sum of angles in a triangle is $180^\circ$.
$\angle U = 180^\circ - 66^\circ - 77^\circ = 37^\circ$

Step2: Find side length t

Use the Law of Sines: $\frac{t}{\sin T} = \frac{TV}{\sin U}$
$\frac{t}{\sin 66^\circ} = \frac{8}{\sin 37^\circ}$
$t = \frac{8 \times \sin 66^\circ}{\sin 37^\circ} \approx \frac{8 \times 0.9135}{0.6018} \approx 12.1$

Step3: Find side length v

Use the Law of Sines: $\frac{v}{\sin V} = \frac{TV}{\sin U}$
$\frac{v}{\sin 77^\circ} = \frac{8}{\sin 37^\circ}$
$v = \frac{8 \times \sin 77^\circ}{\sin 37^\circ} \approx \frac{8 \times 0.9744}{0.6018} \approx 12.9$

Answer:

$\angle U = 37^\circ$, $t \approx 12.1$, $v \approx 12.9$