Question

In ΔCDE, the measure of ∠E=90°, the measure of ∠C=16°, and EC = 65 feet. Find the length of DE to the nearest tenth of a foot.

Answer 1

Given:

Given that the triangle CDE is a right triangle.

The measure of ∠E is 90° and the measure of ∠C is 16° and the length of EC is 65 feet.

We need to determine the length of DE.

Length of DE:

The length of DE can be determined using the trigonometric ratio.

Thus, we have;

`tan \ \theta=(opp)/(adj)`

where the angle is 16° and the side opposite to the angle is DE and the side adjacent to the angle is EC.

Substituting the sides, we get;

`tan \ 16^(\circ)=(DE)/(EC)`

Substituting DE = 65, we have;

`tan \ 16^(\circ)=(DE)/(65)`

Multiplying both sides by 65, we have;

`tan \ 16^(\circ) * 65=DE`

`0.2867 * 65=DE`

`18.6=DE`

Thus, the length of DE is 18.6 feet.