Question

find m∠d.

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

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle \( \triangle CED \) with \( \angle E = 90^{\circ} \), \( CE = 2.4 \), and \( DE = 4.3 \). To find \( m\angle D \), we can use the tangent function. The tangent of an angle in a right - triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. For \( \angle D \), the opposite side is \( CE = 2.4 \) and the adjacent side is \( DE = 4.3 \). So, \( \tan(\angle D)=\frac{CE}{DE}=\frac{2.4}{4.3} \)

Step2: Calculate the angle

We know that if \( \tan(\theta)=\frac{2.4}{4.3}\approx0.5581 \), then \( \theta=\arctan(0.5581) \). Using a calculator to find the arctangent of \( 0.5581 \), we get \( \theta\approx29.1^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 29.1 \)