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Consider triangle XYZ, a right triangle with angle Y at 94 degrees and angle X at 32 degrees. The opposite side XY is 24 units. What is the approximate length of side YZ?

A. 13.3 units
B. 15.7 units
C. 47.1 units
D. 38.2 units

Answer :

Final answer:

The length of side YZ in the right triangle XYZ is approximately 15.7 units, assuming a typo in the given information about angle Y and using the tangent function of angle X with the given adjacent side length. So the correct option is b.

Explanation:

The question asks to find the length of side YZ in a right triangle XYZ given that angle Y is 94 degrees, angle X is 32 degrees, and side XY is 24 units. The sum of angles in a triangle is 180 degrees, but since angle Y is given as 94 degrees, there must be a typo as this would not allow for a right triangle. Assuming angle Y is 90 degrees, to find side YZ, we can use the trigonometric function called the tangent. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. In this case, we use angle X which is 32 degrees.

Using the formula tan(X) = opposite/adjacent, we have:

tan(32°) = YZ/24

To solve for YZ, we multiply both sides of the equation by 24:

YZ = 24 * tan(32°)

Calculating this gives us an approximate length:

YZ ≈ 24 * tan(32°) ≈ 15.7 units

Therefore, the approximate length of side YZ is 15.7 units, which corresponds to option (b).

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