Option C:
[tex]\frac{10}{\sin 29^{\circ}}[/tex] can be used to find the length of PQ.
Solution:
Given PQR is a right triangle.
θ = m∠Q = 29°
Opposite of θ = PR = 10
Hypotenuse = PQ = ?
To find the length of PQ:
Using trigonometric ratio formula:
[tex]$\sin \theta=\frac{\text { Opposite side of } \theta}{\text { Hypotenuse }}[/tex]
[tex]$\sin \theta=\frac{PR}{PQ}[/tex]
[tex]$\sin 29^\circ=\frac{10}{PQ}[/tex]
Multiply by PQ on both sides.
[tex]$PQ \times \sin 29^\circ=\frac{10}{PQ} \times PQ[/tex]
[tex]$PQ \times \sin 29^\circ=10[/tex]
Divide by sin 29° on both sides.
[tex]$\frac{PQ \times \sin 29^\circ}{ \sin 29^\circ} =\frac{10}{ \sin 29^\circ}[/tex]
[tex]$PQ=\frac{10}{ \sin 29^\circ}[/tex]
Therefore [tex]\frac{10}{\sin 29^{\circ}}[/tex] can be used to find the length of PQ.
Option C is the correct answer.
