High School

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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.

Learn more about triangle

brainly.com/question/12113882

#SPJ11

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada