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What is the numerical value of the length |QR|? 100 points and brainy if answer.​

What is the numerical value of the length |QR|? 100 points and brainy if answer.​-example-1
User Michael Westwort
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1 Answer

19 votes
19 votes

Answer:

QR is approximately 20.6.

Explanation:

Look at the right triangle SRQ.

In that triangle we know that:

SQ = 55

m∠QSR = 22°

Choosing angle QSR as a reference angle, QR is opposite side and SQ is hypotenuse.

Which of the trigonometrical functions use opposite and hypotenuse?

Recall SOH CAH TOA - SineOppositeHypotenuse CosineAdjacentHypotnuse TangentOppositeAdjacent

Sine uses both opposite and hypotenuse.


sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}

Aply the formula.


\sin{(m\angle\text{QSR})} = \frac{\text{QR}}{\text{SQ}}


sin(22^\circ) = \frac{\text{QR}}{55}

Multiply with 55 to get rid of the fraction and isolate QR.


sin(22^\circ) \cdot 55 = \frac{\text{QR}}{55}\cdot 55


sin(22^\circ) \cdot 55 = \text{QR}


\text{QR} \approx 20.6

User Eryc
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3.1k points