Question

Given right triangle DEF, what is the value of sin(E)?

A. 3/5
B. 3/4
C. 4/5
D. 4/3

Answer 1

The correct answer is option A. 3/5

Explanation:

Pythagorean theorem:-

Hypotenuse² = Base² + Height²

Trigonometric ratio:-

Sin(∅) = Opposite side / Hypotenuse

It is given a right angled triangle DEF.

DE = 8 and FE = 10

To find the length of DF

Hypotenuse² = Base² + Height²

FE² = DF² + DE²

DF² = FE² - DE² = 10² - 8² = 100 - 64 = 36

DF =√36 = 6

To find Sin(E)

Sin(E) = Opposite side / Hypotenuse = DF/EF = 6/10 =3/5

Sin(E) = 3/5

The correct answer is option A. 3/5

Answer 2

Answer: OPTION A.

Explanation:

First you must calculate the lenght of the side DF by applying the Pythagorean theorem, as following:

`DE=\sqrt{10^(2)-8^(2)}=6`

Now you can find sin(E) as you can see below:

`sin\alpha=opposite/hypotenuse`

Where:

`\alpha=E\\opposite=DF=6\\hypotenuse=EF=10`

Then:

`sin(E)=6/10`

`sin(E)=3/5`