Answer:
[tex]\displaystyle \sin(D)=\frac{28}{53}\approx0.5283[/tex]
[tex]\displaystyle \sin(E)=\frac{45}{53}\approx0.8491[/tex]
Step-by-step explanation:
Remember that sine is the ratio of the opposite side to its hypotenuse:
[tex]\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
For D, the opposite side to D is 28, and the hypotenuse is 53. Therefore:
[tex]\displaystyle \sin(D)=\frac{28}{53}[/tex]
Or, in decimal form:
[tex]\sin(D)\approx 0.5283[/tex]
Likewise, the side opposite to E is 45, and the hypotenuse is 53. Therefore:
[tex]\displaystyle \sin(E)=\frac{45}{53}[/tex]
And using a calculator:
[tex]\sin(E)\approx0.8491[/tex]
