Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.
t =
u =
m∠u =

Explanation:

Step1: Find angle U

The sum of angles in a triangle is 180°. So, $m\angle U=180^{\circ}-125^{\circ}-12^{\circ}=43^{\circ}$.

Step2: Use the Law of Sines to find side t

The Law of Sines states that $\frac{t}{\sin T}=\frac{s}{\sin S}=\frac{u}{\sin U}$. We know $s = 10$, $T = 12^{\circ}$, $S=125^{\circ}$. So, $\frac{t}{\sin12^{\circ}}=\frac{10}{\sin125^{\circ}}$. Then $t=\frac{10\times\sin12^{\circ}}{\sin125^{\circ}}$. Using a calculator, $\sin12^{\circ}\approx0.208$, $\sin125^{\circ}\approx0.819$. So $t=\frac{10\times0.208}{0.819}\approx2.5$.

Step3: Use the Law of Sines to find side u

Using $\frac{u}{\sin U}=\frac{s}{\sin S}$, we have $\frac{u}{\sin43^{\circ}}=\frac{10}{\sin125^{\circ}}$. Then $u = \frac{10\times\sin43^{\circ}}{\sin125^{\circ}}$. Since $\sin43^{\circ}\approx0.682$, $u=\frac{10\times0.682}{0.819}\approx8.3$.

Answer:

$t\approx2.5$
$u\approx8.3$
$m\angle U = 43$