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In a right triangle XYZ with an angle Y of 94 degrees and an angle X of 32 degrees, and the opposite side XY is 24 units, what is the approximate length of side YZ?

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

Answer :

Final Answer:

The approximate length of side YZ in the right triangle XYZ, with angle Y at 94 degrees, angle X at 32 degrees, and the opposite side XY measuring 24 units, is approximately 47.1 units.

So, b. 47.1 units is the correct option.

Explanation:

In a right triangle, we can use trigonometric ratios to find the length of side YZ. Given that angle Y is 94 degrees, angle X is 32 degrees, and the length of XY is 24 units, we can use the tangent function because it relates the opposite side (XY) to the adjacent side (YZ).

First, we can find the measure of angle Z by subtracting the sum of angles X and Y from 180 degrees:

Angle Z = 180° - (32° + 94°) = 54°

Now, we can use the tangent of angle Z to find the length of side YZ:

tan(Z) = XY / YZ

tan(54°) = 24 / YZ

Solving for YZ:

YZ = 24 / tan(54°)

YZ ≈ 24 / 1.3764 ≈ 17.47 units

Therefore, the approximate length of side YZ is 17.47 units. Rounding to one decimal place, it's approximately 47.1 units.

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