Question

The law of cosines is used to find the measure of Angle Q. Triangle Q R S is shown. The length of Q R is 20, the length of R S is 24, and the length of Q S is 34. To the nearest whole degree, what is the measure of Angle Q? 44º 49º 54º 59º

Answer 1

Short and sweet... 44º

Explanation:

:)

Answer 2

44º

Explanation:

We are given that a triangle QRS

QR=20 units

RS=24 units

QS=34 units

We have to find the measure of angle Q.

We know that cosine law

`a^2=b^2+c^2-2bc cos A`

Using the formula

`(24)^2=(20)^2+(34)^2-2* 20* 34 cos Q`

`576=1556-1360 cosQ`

`1360osQ=1556-576`

`1360 cos Q=980`

`cos Q=(980)/(1360)`

`cos Q=0.72`

`Q=cos^(-1)(0.72)`

`Q=44^(\circ)(approx)`