Question

In ΔPQR, the measure of ∠R=90°, QP = 73, PR = 48, and RQ = 55. What ratio represents the sine of ∠Q?

Answer 1

Answer:

$sin(Q)=\frac{48}{73}$

Step-by-step explanation:

we know that

In the right triangle PQR

$sin(Q)=\frac{PR}{QP}$ ----> by SOH (opposite side divided by the hypotenuse)

see the attached figure to better understand the problem

substitute the given values

$sin(Q)=\frac{48}{73}$

Answer 2

We can use sine ratio in given right angled triangle.

The sine of ∠Q is represented by ratio $\dfrac{48}{73}$

Given data:

• ∠R=90°,
• QP = 73,
• PR = 48,
• RQ = 55

What is sine ratio?

The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.

Since against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.

Thus, we have:

$sin(\angle Q) = \dfrac{PR}{PQ} = \dfrac{48}{73}$

Thus, the sine of ∠Q is represented by ratio  $\dfrac{48}{73}$

Learn more about sine function here:

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