Question

find m∠v.
t
9
u
9√3
v
m∠v = °
submit

Explanation:

Step1: Identify triangle type

Triangle \( TUV \) is right - angled at \( U \), so we can use trigonometric ratios. Let's recall that in a right - triangle, \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle V \), the opposite side to \( \angle V \) is \( TU = 9 \) and the adjacent side is \( UV=9\sqrt{3} \).

Step2: Apply tangent ratio

We know that \( \tan(\angle V)=\frac{TU}{UV} \). Substituting the values of \( TU = 9 \) and \( UV = 9\sqrt{3} \), we get \( \tan(\angle V)=\frac{9}{9\sqrt{3}} \). Simplify the right - hand side: \( \frac{9}{9\sqrt{3}}=\frac{1}{\sqrt{3}} \).

Step3: Find the angle

We know that if \( \tan\theta=\frac{1}{\sqrt{3}} \), then from the trigonometric values of special angles, \( \theta = 30^{\circ} \) (since \( \tan30^{\circ}=\frac{1}{\sqrt{3}} \)).

Answer:

\( 30 \)