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In right triangle XYZ, angle Z is a right angle, m angle Y = 16 degrees, and XY = 7. What is the measurement of YZ?

a) 5.12 units
b) 6.08 units
c) 7.00 units
d) 8.26 units

1 Answer

2 votes

Final answer:

The length of side YZ can be calculated using the sine function. Sin(16°) multiplied by the hypotenuse (7 units) results in approximately 1.932 units, which does not match the answer choices provided.

Step-by-step explanation:

In right triangle XYZ, where angle Z is a right angle, we know that angle Y is 16 degrees and the length of hypotenuse XY is 7 units. To find the length of side YZ, we can use the sine function, since sine is defined as the opposite side over the hypotenuse in a right triangle. In this case, the sine of angle Y will give us the length of side YZ divided by the hypotenuse XY.

The formula is as follows:

sin(Y) = YZ/XY

Plugging in the values we know:

sin(16°) = YZ/7

To solve for YZ, we multiply both sides by 7:

YZ = 7 * sin(16°)

Using a calculator, sin(16°) ≈ 0.276.

Therefore:

YZ = 7 * 0.276

YZ = 1.932

After calculating, we see that none of the answer choices (a) through (d) match our result. It seems there might be a mistake in the provided answer choices or the question might have some typos. Usually, for mistakes or uncertainties, it is best to communicate with the student and clarify the discrepancy.

User Olle Kyrychenko
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