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In /_\UVW,u=63 inches, v=91 inches and w=60 inches. Find the measure of /_W to the nearest degree.

In ∠UVW\angle UVW, u=63u=63 inches, v=91v=91 inches and w=60w=60 inches. Find the measure of ∠W\angle W to the nearest degree.

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Full solution

Q. In ∠UVW\angle UVW, u=63u=63 inches, v=91v=91 inches and w=60w=60 inches. Find the measure of ∠W\angle W to the nearest degree.
  1. Use Law of Cosines: Use the Law of Cosines to find angle WW. The formula is cos⁡(W)=u2+v2−w22uv\cos(W) = \frac{u^2 + v^2 - w^2}{2uv}.
  2. Calculate Values: Plug in the values: u=63u = 63 inches, v=91v = 91 inches, w=60w = 60 inches. Calculate u2u^2, v2v^2, and w2w^2. u2=3969u^2 = 3969, v2=8281v^2 = 8281, w2=3600w^2 = 3600.
  3. Substitute into Formula: Substitute these values into the formula: cos⁡(W)=(3969+8281−3600)(2×63×91)\cos(W) = \frac{(3969 + 8281 - 3600)}{(2 \times 63 \times 91)}.
  4. Simplify Numerator: Simplify the numerator: 3969+8281−3600=86503969 + 8281 - 3600 = 8650.
  5. Calculate Denominator: Calculate the denominator: 2×63×91=114662 \times 63 \times 91 = 11466.
  6. Divide Numerator by Denominator: Divide the numerator by the denominator: cos⁡(W)=865011466≈0.754\cos(W) = \frac{8650}{11466} \approx 0.754.
  7. Find Angle WW: Use the inverse cosine function to find WW: W=cos⁡−1(0.754)W = \cos^{-1}(0.754). Calculate W≈41W \approx 41 degrees.

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