Question

find m∠u.
v
15√2
u 30√2 w
m∠u = °
submit

Explanation:

Step1: Identify triangle type

Triangle \( UVW \) is right - angled at \( V \), so we can use trigonometric ratios. Let's recall the sine, cosine, and tangent ratios. The side opposite \( \angle U \) is \( VW = 15\sqrt{2}\), the hypotenuse \( UW=30\sqrt{2}\).

Step2: Use sine ratio

The sine of an angle in a right - triangle is defined as \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). For \( \angle U \), \( \sin(\angle U)=\frac{VW}{UW}\). Substitute \( VW = 15\sqrt{2}\) and \( UW = 30\sqrt{2}\) into the formula:
\( \sin(\angle U)=\frac{15\sqrt{2}}{30\sqrt{2}} \)
Simplify the right - hand side: The \( \sqrt{2} \) terms cancel out, and \( \frac{15}{30}=\frac{1}{2} \). So \( \sin(\angle U)=\frac{1}{2} \).
We know that if \( \sin(\theta)=\frac{1}{2} \) and \( \theta \) is an acute angle (since it's an angle in a right - triangle), then \( \theta = 30^{\circ} \) because \( \sin(30^{\circ})=\frac{1}{2} \).

Answer:

\( 30 \)