Question

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

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right triangle \( \triangle CED \) with right angle at \( E \). To find \( m\angle C \), we can use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. For \( \angle C \), the opposite side is \( ED = 4.5 \) and the adjacent side is \( CE = 3.4 \). So, \( \tan(\angle C)=\frac{ED}{CE}=\frac{4.5}{3.4} \).

Step2: Calculate the angle

First, calculate \( \frac{4.5}{3.4}\approx1.3235 \). Then, take the arctangent (inverse tangent) of this value to find \( \angle C \). Using a calculator, \( \angle C=\arctan(1.3235) \). Calculating this, we get approximately \( 52.9^\circ \) (rounded to the nearest tenth).

Answer:

\( 52.9 \)