Question

In UVW, where the measure of angle W is 90°, VU = 61, UW = 60, and WV = 11, what ratio represents the cotangent of U?

a) 61/60
b) 60/11
c) 11/60
d) 60/61

Answer 1

The given triangle is not possible in Euclidean geometry, therefore the cotangent of angle U cannot be determined.

Step-by-step explanation:

To find the cotangent of angle U in triangle UVW, we need to determine the ratio of the length of the adjacent side to the length of the opposite side. Since the measure of angle W is 90°, we can use the Pythagorean theorem to find the length of side VW:

VW = √(UW^2 - VU^2)

VW = √(60^2 - 61^2)

VW = √(3600 - 3721)

VW = √(-121)

This implies that side VW has an imaginary length, which means that triangle UVW is not possible in Euclidean geometry. Therefore, the cotangent of angle U cannot be determined using the given information.