Question

find the sine of ∠r.
triangle with right angle at q, rq=16, rs=34, vertices r, q, s
simplify your answer and write it as a proper fraction, improper fraction, or whole number.
sin(r) =
fraction and square root buttons

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle R$, opposite side is $SQ$, hypotenuse is $RS = 34$. First, find $SQ$ using Pythagoras: $SQ = \sqrt{34^2 - 16^2} = \sqrt{1156 - 256} = \sqrt{900} = 30$.

Step2: Calculate $\sin(R)$

$\sin(R) = \frac{\text{opposite to } R}{\text{hypotenuse}} = \frac{SQ}{RS} = \frac{30}{34} = \frac{15}{17}$.

Answer:

$\frac{15}{17}$