In ΔVWX, ∠X measures 90°, VX = 35, XW = 12, and WV = 37. What is the value of cos(∠W) to the nearest hundredth?
Mathematics · High School · Thu Feb 04 2021
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Answer: To find the cosine of ∠W in ΔVWX, we can use the definition of cosine in a right triangle. The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse.
According to the given information, ΔVWX is a right triangle with ∠X being the right angle. Therefore, VX is the side opposite to ∠W, XW is the side adjacent to ∠W, and WV is the hypotenuse of the triangle.
The cosine of ∠W is given by the ratio of the length of the adjacent side to the length of the hypotenuse: cos(∠W) = XW / WV
Given: XW = 12 (Adjacent side to ∠W) WV = 37 (Hypotenuse)
Plugging in these values: cos(∠W) = 12 / 37 ≈ 0.3243 (rounded to the nearest hundredth)
Therefore, the cosine of ∠W is approximately 0.32 to the nearest hundredth.