Answer:
Y = 32.7°
Step-by-step explanation:
We will apply the Cosine law in the given triangle XYZ,
x = 90 ft
y = 55 ft
z = 50 ft
We have to find the measure of angle Y.
y² = x² + z² - 2xzCosY
(55)² = (90)² + (50)² - 2(90)(50)cosY
3025 = 8100 + 2500 - 9000.cosY
9000.cosY = 10600 - 3025
cosY = [tex]\frac{7575}{9000}[/tex]
= 0.84167
Y = [tex]\text{cos}^{-1}(0.84167)[/tex]
Y = 32.68 ≈ 32.7°
Therefore, measure of angle Y = 32.7°
