Final answer:
To find the length of side YZ in triangle XYZ, use the sine function with angle X, which gives YZ ≈ 6.8 feet. The answer is option (a).
Step-by-step explanation:
To find the length of YZ in triangle XYZ, where angle Z is a right angle (90°), angle X is 57°, and the length of XY is 8 feet, we can use the trigonometric functions. Since we are given angle X and want to find the length opposite to it (YZ), we use the sine function:
sin(X) = opposite/hypotenuse
sin(57°) = YZ/XY
Substitute the given values:
sin(57°) = YZ/8
Now, solve for YZ:
YZ = 8 × sin(57°)
Using a calculator, find sin(57°) and multiply by 8 to get the length of YZ to the nearest tenth of a foot.
The calculation yields YZ ≈ 6.8 feet.
Therefore, the correct answer is (a) 6.8 feet.