Question

find t.
write your answer as an integer or as a decimal rounded to the nearest tenth.
t =
submit

Explanation:

Step1: Find the measure of angle \( U \)

By the triangle - angle sum theorem (\( \angle V+\angle T+\angle U = 180^{\circ} \)).
Given \( \angle V = 31^{\circ} \) and \( \angle T=87^{\circ} \), then \( \angle U=180^{\circ}-(31^{\circ}+87^{\circ})=62^{\circ} \).

Step2: Apply the Law of Sines

The Law of Sines states that \( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \).
In \( \triangle TUV \), if we let \( a = t\), \(A=\angle T = 87^{\circ}\), \(b = 7\), \(B=\angle U=62^{\circ}\), then \( \frac{t}{\sin87^{\circ}}=\frac{7}{\sin62^{\circ}} \).
Since \( \sin87^{\circ}\approx0.9986 \) and \( \sin62^{\circ}\approx0.8829 \), we can solve for \( t \):
\( t=\frac{7\times\sin87^{\circ}}{\sin62^{\circ}} \).
Substitute the sine values: \( t=\frac{7\times0.9986}{0.8829} \).
\( t=\frac{6.9902}{0.8829}\approx7.9 \).

Answer:

\( t = 7.9 \)