Question

find m∠c.

b ---- 7.4 ---- c
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a
(with a right angle at a, and ab = 4.7)

write your answer as an integer or as a decimal rounded to the nearest tenth.

m∠c = \boxed{\space}°

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle with right angle at \(A\). We know the lengths of the opposite side (\(AB = 4.7\)) and the hypotenuse (\(BC=7.4\)) with respect to \(\angle C\). The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(\angle C)=\frac{AB}{BC}=\frac{4.7}{7.4}\).

Step2: Calculate the angle

First, calculate \(\frac{4.7}{7.4}\approx0.6351\). Then, to find \(\angle C\), we take the inverse sine (arcsin) of \(0.6351\). Using a calculator, \(\angle C=\arcsin(0.6351)\). Calculating this, we get \(\angle C\approx39.4^{\circ}\) (rounded to the nearest tenth).

Answer:

\(39.4\)