Answer:
QR is approximately 20.6.
Step-by-step 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.
[tex]\sin{\theta} = \frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Aply the formula.
[tex]\sin{(m\angle\text{QSR})} = \frac{\text{QR}}{\text{SQ}}[/tex]
[tex]\sin{22^\circ} = \frac{\text{QR}}{55}[/tex]
Multiply with 55 to get rid of the fraction and isolate QR.
[tex]\sin{22^\circ} \cdot 55 = \frac{\text{QR}}{55}\cdot 55[/tex]
[tex]\sin{22^\circ} \cdot 55 = \text{QR}[/tex]
[tex]\text{QR} \approx 20.6[/tex]
