Question

find m∠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

This is a right - triangle \( \triangle UTS \) with \( \angle T = 90^{\circ} \), hypotenuse \( US = 7 \), and opposite side to \( \angle S \) is \( UT = 5 \). We use the sine function, where \( \sin(\angle S)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{UT}{US} \).

Step2: Calculate the sine of \( \angle S \)

Substitute the values: \( \sin(\angle S)=\frac{5}{7}\approx0.7143 \).

Step3: Find \( \angle S \)

Take the inverse sine (arcsin) of \( 0.7143 \): \( \angle S=\arcsin(0.7143) \). Using a calculator, \( \angle S\approx45.6^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 45.6 \)