Question

find m∠y.
x----y
5.7 4.3
w (right angle at w)
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠y = \boxed{}°

Explanation:

Step1: Identify triangle type

Triangle \( XWY \) is right - angled at \( W \), so we can use trigonometric ratios. In right - triangle \( XWY \), for angle \( Y \), the opposite side to \( \angle Y \) is \( XW = 5.7 \) and the adjacent side to \( \angle Y \) is \( WY=4.3 \).
We know that the tangent of an angle \( \theta \) in a right - triangle is given by \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(\angle Y)=\frac{XW}{WY}=\frac{5.7}{4.3} \).

Step2: Calculate the angle

First, calculate \( \frac{5.7}{4.3}\approx1.3256 \). Then, to find \( \angle Y \), we take the arctangent (inverse tangent) of \( 1.3256 \). Using a calculator, \( \angle Y=\arctan(1.3256) \).
Calculating \( \arctan(1.3256) \), we get approximately \( 53.0^\circ \) (rounded to the nearest tenth).

Answer:

\( 53.0 \)