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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

2 Answers

13 votes

Answer:

Short and sweet... 44º

Explanation:

:)

User Mrdavidjcole
by
8.0k points
1 vote

Answer:

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)

The law of cosines is used to find the measure of Angle Q. Triangle Q R S is shown-example-1
User Eliza Brock Marcum
by
8.3k points

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