Question

find de.

triangle def with right angle at d, angle at e is 27 degrees, hypotenuse ef is 6.7

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

de =

submit

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( DEF \), \( \angle E = 27^\circ \), hypotenuse \( EF = 6.7 \), and we need to find \( DE \) (adjacent side to \( \angle E \)). We use the cosine function: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
So, \( \cos(27^\circ) = \frac{DE}{EF} \).

Step2: Solve for \( DE \)

Substitute \( EF = 6.7 \) into the equation: \( DE = 6.7 \times \cos(27^\circ) \).
Calculate \( \cos(27^\circ) \approx 0.891 \), then \( DE \approx 6.7 \times 0.891 \approx 6.0 \).

Answer:

\( 6.0 \)