Question

find m∠c.
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠c = \boxed{}°

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle \( \triangle BCD \) with \( \angle B = 90^\circ \), \( BC = 7.1 \), and \( CD = 9.5 \) (hypotenuse). To find \( \angle C \), we can use the cosine ratio since \( \cos(\angle C)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{BC}{CD} \).

Step2: Calculate the cosine value

Substitute the values: \( \cos(\angle C)=\frac{7.1}{9.5} \approx 0.7474 \).

Step3: Find the angle using inverse cosine

Take the inverse cosine: \( \angle C=\cos^{-1}(0.7474) \). Using a calculator, \( \angle C\approx 41.6^\circ \) (rounded to the nearest tenth).

Answer:

\( 41.6 \)