Question

in δvwx, v = 52 inches, w = 62 inches and x = 75 inches. find the measure of ∠x to the nearest 10th of a degree.

Explanation:

Step1: Apply Law of Cosines

$\cos(X) = \frac{v^2 + w^2 - x^2}{2vw}$

Step2: Substitute given values

$\cos(X) = \frac{52^2 + 62^2 - 75^2}{2\times52\times62}$

Step3: Calculate numerator/denominator

$\cos(X) = \frac{2704 + 3844 - 5625}{6448} = \frac{923}{6448} \approx 0.1431$

Step4: Find inverse cosine

$X = \cos^{-1}(0.1431) \approx 42.9^\circ$

Answer:

42.9 degrees