Question

find m∠s. t r 8.6 10 s write your answer as an integer or as a decimal rounded to the nearest tenth. m∠s = °

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle \( \triangle STR \) with \( \angle T = 90^\circ \), \( ST = 8.6 \), and \( SR = 10 \). To find \( m\angle S \), we can use the cosine ratio since \( \cos(\angle S)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{ST}{SR} \).

Step2: Calculate the cosine value

Substitute the values: \( \cos(\angle S)=\frac{8.6}{10} = 0.86 \).

Step3: Find the angle using inverse cosine

Take the inverse cosine (arccos) of \( 0.86 \): \( \angle S=\arccos(0.86) \). Using a calculator, \( \arccos(0.86)\approx 30.6^\circ \) (rounded to the nearest tenth).

Answer:

\( 30.6 \)