Question

find cd.

triangle image with right angle at e, de = 6, angle at d is 40 degrees

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

submit

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( CDE \), \( \angle E = 90^\circ \), \( \angle D = 40^\circ \), and \( DE = 6 \). We need to find \( CD \) (the hypotenuse). We can use the cosine function, where \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). Here, \( \cos(40^\circ)=\frac{DE}{CD} \), so \( CD = \frac{DE}{\cos(40^\circ)} \).

Step2: Substitute the values and calculate

We know \( DE = 6 \) and \( \cos(40^\circ)\approx0.7660 \). So \( CD=\frac{6}{0.7660}\approx7.8 \).

Answer:

\( 7.8 \)