Question

find ( mangle w ).

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle w = square^circ )

Explanation:

Step1: Apply Law of Cosines

$\cos(\angle W) = \frac{WX^2 + WV^2 - XV^2}{2 \cdot WX \cdot WV}$

Step2: Substitute side lengths

$\cos(\angle W) = \frac{24^2 + 14^2 - 13^2}{2 \cdot 24 \cdot 14}$

Step3: Calculate numerator/denominator

$\cos(\angle W) = \frac{576 + 196 - 169}{672} = \frac{603}{672} \approx 0.8973$

Step4: Find inverse cosine

$\angle W = \cos^{-1}(0.8973)$

Answer:

$30.8^\circ$