Question

find m∠y.
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠y = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle XWY \) with right angle at \( W \). We know the lengths of the opposite side (\( XW = 3 \)) and the adjacent side (\( WY=7 \)) to angle \( Y \). The tangent of an angle in a right - triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. So, \( \tan(Y)=\frac{\text{opposite}}{\text{adjacent}}=\frac{XW}{WY} \)

Step2: Calculate the tangent value

Substitute \( XW = 3 \) and \( WY = 7 \) into the tangent formula: \( \tan(Y)=\frac{3}{7}\approx0.4286 \)

Step3: Find the angle measure

To find the measure of angle \( Y \), we take the arctangent (inverse tangent) of \( 0.4286 \). Using a calculator, \( Y=\arctan(0.4286) \). Calculating this, we get \( Y\approx23.2^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 23.2 \)