Question

find m∠x.

write your answer as an integer or as a decimal rounded to the nearest tenth.

m∠x = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

Triangle \( WXY \) is right - angled at \( W \). We know the lengths of the opposite side (\( WY = 8 \)) and the adjacent side (\( WX=4 \)) to angle \( X \). The tangent function is defined as \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(\angle X)=\frac{WY}{WX}=\frac{8}{4} = 2 \).

Step2: Find the angle using arctangent

To find \( \angle X \), we take the arctangent (inverse tangent) of 2. Using a calculator, \( \angle X=\arctan(2) \). Calculating this, \( \arctan(2)\approx63.4^\circ \) (rounded to the nearest tenth).

Answer:

\( 63.4 \)