Question

In triangle AUVW, the measure of angle ZW is 90°, VU = 65, UW = 33, and WV = 56. What ratio represents the tangent of angle ZU?

A) tan(ZU) = 56/65
B) tan(ZU) = 33/65
C) tan(ZU) = 56/33
D) tan(ZU) = 33/56

Answer 1

The tangent of angle ZU is the ratio of the opposite side (UW) to the adjacent side (VU) which is 33/65, making option B correct.

The correct option is B.

Step-by-step explanation:

To find the tangent of angle ZU in triangle AUVW, we first have to identify which sides of the triangle are adjacent and opposite to our angle of interest. The naming of angles and sides seems to be non-standard here, so let us work with the information provided: VU = 65, UW = 33, and WV = 56.

We're also told that angle ZW is 90°, which implies that we have a right triangle, and ZW is the hypotenuse. If angle ZU refers to the angle at point U, then the tangent of angle ZU (tan(ZU)) is the ratio of the opposite side to the adjacent side.

Since UW is the side opposite to angle ZU, and VU is the side adjacent to angle ZU, the tangent of angle ZU is UW/VU, which is 33/65. Therefore, tan(ZU) = 33/65, which matches option B. We're using the definition of the tangent function in a right triangle, which states tan(θ) = opposite/adjacent.

The correct option is B.