Question

solve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
wx=

m∠x=

m∠y=

Explanation:

Step1: Find \( WX \) using Pythagorean theorem

In a right - triangle \( \triangle WXY \), by the Pythagorean theorem \( WX=\sqrt{XY^{2}-WY^{2}} \). Given \( XY = 10 \) and \( WY=9 \), then \( WX=\sqrt{10^{2}-9^{2}}=\sqrt{100 - 81}=\sqrt{19}\approx4.4 \).

Step2: Find \( m\angle Y \) using cosine function

\(\cos Y=\frac{WY}{XY}\). Substitute \( WY = 9 \) and \( XY = 10 \), so \(\cos Y=\frac{9}{10}=0.9\). Then \(m\angle Y=\cos^{-1}(0.9)\approx26^{\circ}\).

Step3: Find \( m\angle X \) using the angle - sum property of a triangle

Since the sum of angles in a triangle is \(180^{\circ}\) and the triangle is right - angled (\(m\angle W = 90^{\circ}\)), \(m\angle X=180^{\circ}-(m\angle Y + m\angle W)\). Substitute \(m\angle Y\approx26^{\circ}\) and \(m\angle W = 90^{\circ}\), so \(m\angle X=180^{\circ}-(26^{\circ}+90^{\circ}) = 64^{\circ}\).

Answer:

\(m\angle Y = 26^{\circ}\), \(m\angle X=64^{\circ}\), \(WX = 4.4\)