Question

solve the right triangle.
v 31° t
√71
u
write your answers as integers or as decimals rounded to the nearest tenth.
tu =
tv =
m∠u = °
submit

Explanation:

Step1: Find \( m\angle U \)

In a right triangle, the sum of the acute angles is \( 90^\circ \). Given \( \angle V = 31^\circ \), so \( m\angle U = 90^\circ - 31^\circ = 59^\circ \).

Step2: Find \( TU \)

In right triangle \( VTU \), \( \sin(31^\circ)=\frac{TU}{VU} \), and \( VU = \sqrt{71} \approx 8.426 \). So \( TU = VU \cdot \sin(31^\circ) \approx 8.426 \cdot 0.515 \approx 4.3 \) (using calculator for \( \sin(31^\circ) \approx 0.515 \)).

Step3: Find \( TV \)

Using \( \cos(31^\circ)=\frac{TV}{VU} \), so \( TV = VU \cdot \cos(31^\circ) \approx 8.426 \cdot 0.857 \approx 7.2 \) (using calculator for \( \cos(31^\circ) \approx 0.857 \)).

Answer:

\( TU \approx 4.3 \)
\( TV \approx 7.2 \)
\( m\angle U = 59^\circ \)