Question

In ΔUVW, u = 94 cm, v = 52 cm and w=92 cm. Find the measure of ∠U to the nearest 10th of a degree.

Answer 1

∠ U ≈ 75.9°

Explanation:

given a triangle where all 3 sides are given

Calculate the measure of ∠ U using the Cosine Rule

cos U =
`(v^2+w^2-u^2)/(2vw)`

given u = 94 , v = 52 , w = 92

substitute these values into the formula for cos U

cos U =
`(52^2+92^2-94^2)/(2(52)(92))` =
`(2704+8464-8836)/(9568)` =
`(2332)/(9568)` , then

∠ U =
`cos^(-1)` (
`(2332)/(9568)` ) ≈ 75.9° ( to the nearest tenth )