Question

In PQR shown below, which expression can be used to find PQ?

Answer 1

Option C:

$\frac{10}{\sin 29^{\circ}}$ 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:

$\sin \theta=\frac{\text { Opposite side of } \theta}{\text { Hypotenuse }}$

$\sin \theta=\frac{PR}{PQ}$

$\sin 29^\circ=\frac{10}{PQ}$

Multiply by PQ on both sides.

$PQ \times \sin 29^\circ=\frac{10}{PQ} \times PQ$

$PQ \times \sin 29^\circ=10$

Divide by sin 29° on both sides.

$\frac{PQ \times \sin 29^\circ}{ \sin 29^\circ} =\frac{10}{ \sin 29^\circ}$

$PQ=\frac{10}{ \sin 29^\circ}$

Therefore $\frac{10}{\sin 29^{\circ}}$ can be used to find the length of PQ.

Option C is the correct answer.