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2 months ago

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What is the approximate angle measure for angle W in the triangle below?

1 answer:

lawyer [12.5K]2 months ago

3 0

Given that we have all three sides of the triangle, we can classify this as a Side-Side-Side (SSS) triangle. To find the angle, we start by applying the Law of Cosines specifically to the side opposite the angle of interest, which is angle W, opposite side XV:
XV² = XW² + WV² - 2(XW)(WV)cos W
Plugging in the known values:
116² = 96² + 89² - 2(96)(89)cos W
Calculating W
13,456 = 9,216 + 7,921 - 17,088 cos W
13,456 = 17,137 - 17,088 cos W
13,456 - 17,137 = 17,137 - 17,088 cos W - 17,137
-3,681 = -17,088 cos W
(-3,681)/(-17,088) = (-17,088 cos W)/(-17,088)
0.215414326 = cos W
cos W = 0.215414326

To find W:
W = cos^(-1)(0.215414326)
Calculating with a calculator:
W ≈ 77.56016397°
Rounded to one decimal place:
W ≈ 77.6°

Answer: The third option, 77.6°

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