Question

Given RQ = 20 inches and PR = 25 inches what is the m∠Q ?

Answer 1

73.2°

Explanation:

Use Law of Sines to solve:

(Sin 50)/20 = (Sin B)/25

Solve for Sin B

[25(Sin 50)]/20 = Sin B

Use Sin^-1 x to solve (sine inverse)

Sin^-1 ( [25(Sin 50)]/20 ) = B

B = 73.24685774

Answer 2

73 degrees

Explanation:

Use the sine law:

`(RQ)/(\sin(\angle P))=(PR)/(\sin(\angle Q))`

We have

`RQ=20\ in\\\\m\angle P=50^o\to\sin50^o\approx0.766\\\\PR=25\ in`

Substitute:

`(20)/(0.766)=(25)/(\sin(\angle Q))` cross multiply

`20\sin(\angle Q)=(25)(0.766)`

`20\sin(\angle Q)=19.15` divide both sides by 20

`\sin(\angle Q)=0.9575\to m\angle Q\approx73^o`