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We have been given that in ΔJKL, the measure of ∠L=90°, KL = 22 feet, and JK = 54 feet. We are asked to find the measure of angle J to nearest degree.
First of all, we will draw a triangle as shown in the attachment.
We can see from our attachment that side KL is opposite side to angle J and side JK is hypotenuse of right triangle.
We know that sine relates opposite side of right triangle to hypotenuse.
![\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}](https://tex.z-dn.net/?f=%5Ctext%7Bsin%7D%3D%5Cfrac%7B%5Ctext%7BOpposite%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D)
![\text{sin}(\angle J)=\frac{22}{54}](https://tex.z-dn.net/?f=%5Ctext%7Bsin%7D%28%5Cangle%20J%29%3D%5Cfrac%7B22%7D%7B54%7D)
Using inverse sine or arcsin, we will get:
![\angle J=\text{sin}^{-1}(\frac{22}{54})](https://tex.z-dn.net/?f=%5Cangle%20J%3D%5Ctext%7Bsin%7D%5E%7B-1%7D%28%5Cfrac%7B22%7D%7B54%7D%29)
![\angle J=24.042075905756^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20J%3D24.042075905756%5E%7B%5Ccirc%7D)
Upon rounding to nearest degree, we will get:
![\angle J\approx 24^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20J%5Capprox%2024%5E%7B%5Ccirc%7D)
Therefore, the measure of angle J is approximately 24 degrees.
Answer:
(a) [8, 14]
(b) ![8 \leq x \leq 14](https://tex.z-dn.net/?f=8%20%5Cleq%20x%20%5Cleq%2014)
(c)See attachment
Step-by-step explanation:
We want to choose a value of x within 3 units of 11.
(a)Now, 11-3=8 and 11+3=14
The possible values of x ranges is in the closed interval [8,14]
(b) Since x is within 3 units of 11., we have:
![|11-x|\leq3](https://tex.z-dn.net/?f=%7C11-x%7C%5Cleq3)
Solving the absolute inequality
![-3 \leq 11-x \leq 3\\$In $ -3 \leq 11-x\\ x \leq 11+3\\x \leq 14\\\\$In $ 11-x \leq 3\\ 11-3 \leq x\\8 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\8 \leq x \leq 14](https://tex.z-dn.net/?f=-3%20%5Cleq%2011-x%20%5Cleq%203%5C%5C%24In%20%24%20-3%20%5Cleq%2011-x%5C%5C%20x%20%5Cleq%2011%2B3%5C%5Cx%20%5Cleq%2014%5C%5C%5C%5C%24In%20%24%2011-x%20%5Cleq%203%5C%5C%2011-3%20%5Cleq%20x%5C%5C8%20%5Cleq%20x%5C%5C%24Therefore%2Can%20inequality%20that%20represents%20all%20values%20of%20x%20that%20meet%20this%20constraint%20is%3A%24%5C%5C8%20%5Cleq%20x%20%5Cleq%2014)
(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.