Question

Triangle X Y Z is shown. Angle X Z Y is 90 degrees and angle X Y Z is 41 degrees. The length of Z X is 22. Which equation could be used to solve for the length of XY?

Answer 1

To find the length of side XY in triangle XYZ, use the trigonometric tangent function with the given angle of 41 degrees and the length of ZX which is 22, resulting in the equation XY = 22 * tan(41°).

Step-by-step explanation:

To solve for the length of XY in right triangle XYZ, where angle XYZ is 41 degrees angle XZY is 90 degrees, and the length of side ZX is 22, we can use trigonometry. Specifically, we can use the trigonometric functions related to a right triangle.

Since XY is the side opposite to angle XYZ, and ZX is the side adjacent to angle XYZ, the tangent function is the most appropriate:

• tangent of angle XYZ = opposite side / adjacent side

In this case:

• tan(41°) = XY / 22

To solve for XY, we rearrange the equation:

• XY = 22 * tan(41°)

This is the equation that can be used to solve for the length of XY.