Answer:
![\displaystyle \sin(D)=\frac{28}{53}\approx0.5283](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28D%29%3D%5Cfrac%7B28%7D%7B53%7D%5Capprox0.5283)
![\displaystyle \sin(E)=\frac{45}{53}\approx0.8491](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28E%29%3D%5Cfrac%7B45%7D%7B53%7D%5Capprox0.8491)
Step-by-step explanation:
Remember that sine is the ratio of the opposite side to its hypotenuse:
![\displaystyle \sin(x^\circ)=\frac{\text{Opposite}}{\text{Hypotenuse}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28x%5E%5Ccirc%29%3D%5Cfrac%7B%5Ctext%7BOpposite%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D)
For D, the opposite side to D is 28, and the hypotenuse is 53. Therefore:
![\displaystyle \sin(D)=\frac{28}{53}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28D%29%3D%5Cfrac%7B28%7D%7B53%7D)
Or, in decimal form:
![\sin(D)\approx 0.5283](https://tex.z-dn.net/?f=%5Csin%28D%29%5Capprox%200.5283)
Likewise, the side opposite to E is 45, and the hypotenuse is 53. Therefore:
![\displaystyle \sin(E)=\frac{45}{53}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28E%29%3D%5Cfrac%7B45%7D%7B53%7D)
And using a calculator:
![\sin(E)\approx0.8491](https://tex.z-dn.net/?f=%5Csin%28E%29%5Capprox0.8491)
Answer: 1.61
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Work Shown:
tan(angle) = opposite/adjacent
tan(J) = IK/IJ
tan(J) = 45/28
tan(J) = 1.60714 approximately
tan(J) = 1.61
<span>The word in question is "starting." Taking away the second "t" gives "staring." Next, taking away the "a" gives "string," and taking away the "r" gives "sting." Further, dropping the second "t" gives "sing." Next, removing the "g" leads to "sin," the "s" gives "in," and finally taking away the "n" leaves the word "I."</span>
Answer:
$69
Step-by-step explanation:
He ows Josue $69 because $158-$89 = $69