Question

In AXYZ, AY=90° and ∠X=58°. ∠ZWY=70° and XW=120. Find the length of ZY to the nearest ioth.

a) 63.4
b) 79.2
c) 90.6
d) 105.8

Answer 1

To find the length of ZY, we can use the sine function to set up an equation and solve for ZY. Using a calculator, we find that ZY is approximately 101.8.

Step-by-step explanation:

In triangle AXYZ, given that AY is a right angle and angle X is 58 degrees, we need to find the length of ZY. To find ZY, we can use the sine function. The sine of angle X is equal to the ratio of the length of the opposing side (ZY) to the hypotenuse (XW). So, we can set up the equation sin(58 degrees) = ZY / 120. Solving for ZY, we get ZY = sin(58 degrees) * 120. Using a calculator, we find that sin(58 degrees) ≈ 0.848. Therefore, ZY ≈ 0.848 * 120 = 101.76. Rounding to the nearest tenth, the length of ZY is approximately 101.8.