Question

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

Answer 1

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`