Question

A triangle was dilated by a scale factor of 2. If cos a° = three fifths and segment FD measures 6 units, how long is segment DE?

Answer 1

Answer:

10 units

Step-by-step explanation:

Given that:

Cos a = 3 /5

From trigonometry ;

Cos θ = Adjacent / hypotenus

Side Adjacent angle a = 3 = FD

Hypotenus = 5 = DE

3 / 5 = FD / DE

FD = 6 units

3/5 = 6/DE

DE * 3/5 = 6

DE = 6 ÷ 3/5

DE = 6 * 5 /3

DE = 30 /3

DE = 10 units

Answer 2

The length of segment DE according to the given information is; 10units

Cosine identity

According to the given information,

• The segment FD is given as 6 units.

• The angle measure a has it's cosine to be; cos a° = three fifths = 3/5.

Hence, the resulting right triangle can be evaluated as follows.

The hypothenuse, segment DE of the resulting triangle can be evaluated as;

Hypothenuse = DE = FD/cos a°

• DE = 6 ÷ 3/5

• DE = 6× 5/3

• DE = 10 units.

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