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4 years ago

Given right triangle DEF, what is the value of sin(E)? A. 3/5 B. 3/4 C. 4/5 D. 4/3

Mathematics

2 answers:

wariber [46]4 years ago

8 0

Answer: OPTION A.

Step-by-step 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:

$sin(E)=6/10$

$sin(E)=3/5$

xenn [34]4 years ago

6 0

Answer:

The correct answer is option A. 3/5

Step-by-step 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

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