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Nadya [2.5K]
3 years ago
14

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.

Mathematics
1 answer:
Eva8 [605]3 years ago
6 0

<u>Given</u>:

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.

<u>Length of DE:</u>

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

Thus, we have;

tan \ \theta=\frac{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}=\frac{DE}{EC}

Substituting DE = 65, we have;

tan \ 16^{\circ}=\frac{DE}{65}

Multiplying both sides by 65, we have;

tan \ 16^{\circ} \times 65=DE

 0.2867 \times 65=DE

             18.6=DE

Thus, the length of DE is 18.6 feet.

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