Question

Find Y.

Round to the nearest tenth.
Z
90 ft
55 ft
X
50 ft
Y
Y= [? ]°
Law of Cosines: c2 = a2 + b2 – 2ab cos C

Answer 1

∠ Y ≈ 32.7°

Explanation:

Using the law of Cosines

cosY =
`(x^2+z^2-y^2)/(2xz)`

with x = 90, y = 55, z = 50

cosY =
`(90^2+50^2-55^2)/(2(90)(50))` =
`(8100+2500-3025)/(9000)` =
`(7575)/(9000)` , then

∠ Y =
`cos^(-1)` (
`(7575)/(9000)` ) ≈ 32.7° ( to the nearest tenth )