Thank you for visiting 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. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
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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