Math / Trigonometry

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In $\triangle \mathrm{QRS}$ , the measure of $\angle S=90^{\circ}, \mathrm{RQ}=61, \mathrm{SR}=11$ , and $\mathrm{QS}=60$ . What ratio represents the sine of $\angle R$ ?

Studdy Solution

STEP 1

1. We have a right triangle $\triangle QRS$ with $\angle S = 90^\circ$ .
2. The sides of the triangle are given as $RQ = 61$ , $SR = 11$ , and $QS = 60$ .
3. We need to find the sine of $\angle R$ .

STEP 2

1. Identify the sides relative to $\angle R$ .
2. Use the definition of sine in a right triangle.
3. Calculate the sine of $\angle R$ .

STEP 3

Identify the sides relative to $\angle R$ : - The side opposite $\angle R$ is $QS = 60$ . - The hypotenuse of the triangle is $RQ = 61$ .

STEP 4

Use the definition of sine in a right triangle: - The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

STEP 5

Calculate the sine of $\angle R$ : - $\sin R = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{QS}{RQ} = \frac{60}{61}$ .
The ratio that represents the sine of $\angle R$ is:
$\boxed{\frac{60}{61}}$

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