Question

In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foo

Answer 1

To find the length of YZ in ΔXYZ, where ∠Z is 90°, ∠X is 57°, and XY is 8 feet, we use the tangent function. By calculating YZ = 8 * tan(57°), we find that the length of YZ is approximately 12.3 feet when rounded to the nearest tenth.

Step-by-step explanation:

In ΔXYZ, we are given that ∠Z is a right angle, ∠X measures 57°, and XY is 8 feet. To find the length of YZ to the nearest tenth of a foot, we can use trigonometric ratios.

Since ∠Z is 90°, ΔXYZ is a right triangle. Therefore, we can use the tangent function, which relates the lengths of the opposite side to the adjacent side of an acute angle in a right triangle. The formula for the tangent of an angle is tan(∠) = opposite/adjacent.

In this case, we want to find the length of YZ (opposite to ∠X), and we know XY (adjacent to ∠X) and that tan(57°) = YZ/8. Solving for YZ, we get:

• 
  
• YZ = 8 * tan(57°)

Using a calculator or a trigonometry table:

• 
  
• tan(57°) ≈ 1.5399
• 
  
• YZ ≈ 8 * 1.5399
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• YZ ≈ 12.3192

Hence, the length of YZ is approximately 12.3 feet, when rounded to the nearest tenth.

Answer 2

9.5 feet

Step-by-step explanation:

We solve this question using Sine rule

XY/sin X = YZ/Sin Z

From the question:

∠Z=90°

∠X=57°

XY = 8 feet.

8/sin 57 = YZ/sin 90

Cross Multiply

sin 57 × YZ = 8 × sin 90

YZ = 8 × sin 90/sin 57

YZ = 9.53891 feet

Approximately = 9.5 feet

Therefore, the length of YZ is 9.5 feet