Question

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

Answer 1

Answer:

73.2°

Step-by-step 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

Answer:

73 degrees

Step-by-step explanation:

Use the sine law:

$\dfrac{RQ}{\sin(\angle P)}=\dfrac{PR}{\sin(\angle Q)}$

We have

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

Substitute:

$\dfrac{20}{0.766}=\dfrac{25}{\sin(\angle Q)}$     cross multiply

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

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

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