Question

find m∠a.

write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠a = °

Explanation:

Step1: Identify triangle type and sides

This is a right triangle \( \triangle ABC \) with \( \angle B = 90^\circ \), hypotenuse \( AC = 7 \), and opposite side to \( \angle A \) is \( BC = 4.6 \). We use the sine function: \( \sin(A)=\frac{\text{opposite}}{\text{hypotenuse}} \).

Step2: Calculate \( \sin(A) \)

\( \sin(A)=\frac{4.6}{7}\approx0.6571 \)

Step3: Find \( \angle A \)

Take the inverse sine: \( A = \arcsin(0.6571)\approx41.1^\circ \)

Answer:

\( 41.1 \)