Question

find the value of sin r rounded to the nearest hundredth, if necessary.

triangle image with right angle at s, side ts = 5, side rs = 12

answer
attempt 1 out of 2

sin r = blank box submit answer button

Explanation:

Step1: Recall SOHCAHTOA for sine

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For angle \( R \), we first need to find the hypotenuse.

Step2: Calculate the hypotenuse \( RT \)

Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( a = 5 \), \( b = 12 \). So \( RT = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \).

Step3: Find \( \sin R \)

The side opposite angle \( R \) is \( ST = 5 \), and the hypotenuse is \( RT = 13 \). Thus, \( \sin R = \frac{5}{13} \approx 0.38 \) (rounded to the nearest hundredth).

Answer:

\( 0.38 \)