Question

HIII! Find Sin D and sin E! Write the answer as a fraction and as a decimal. Round to four decimal places, if necessary! Please help me!

Answer 1

`\displaystyle \sin(D)=(28)/(53)\approx0.5283`

`\displaystyle \sin(E)=(45)/(53)\approx0.8491`

Explanation:

Remember that sine is the ratio of the opposite side to its hypotenuse:

`\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}`

For D, the opposite side to D is 28, and the hypotenuse is 53. Therefore:

`\displaystyle \sin(D)=(28)/(53)`

Or, in decimal form:

`\sin(D)\approx 0.5283`

Likewise, the side opposite to E is 45, and the hypotenuse is 53. Therefore:

`\displaystyle \sin(E)=(45)/(53)`

And using a calculator:

`\sin(E)\approx0.8491`