Answer:
![\theta \approx 82.34^\circ](https://tex.z-dn.net/?f=%5Ctheta%20%5Capprox%2082.34%5E%5Ccirc)
Step-by-step explanation:
Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)
So, we want to find θ.
Since we formed a right triangle, we can use right triangle ratios.
We know the measure of the adjacent side to θ and the hypotenuse.
Therefore, we will use the cosine ratio:
![\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28%5Ctheta%29%3D%5Cfrac%7B%5Ctext%7Badjacent%7D%7D%7B%5Ctext%7Bhypotenuse%7D%7D)
The adjacent side is 2 and the hypotenuse is 15. By substitution:
![\displaystyle \cos(\theta)=\frac{2}{15}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28%5Ctheta%29%3D%5Cfrac%7B2%7D%7B15%7D)
Now, we will take the inverse cosine of both sides. So:
![\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%3D%5Ccos%5E%7B-1%7D%5CBig%28%5Cfrac%7B2%7D%7B15%7D%5CBig%29)
Use a calculator. Hence:
![\theta \approx 82.34^\circ](https://tex.z-dn.net/?f=%5Ctheta%20%5Capprox%2082.34%5E%5Ccirc)
The angle between the ground and the ladder is about 82.34°.
We can find the length of the sides now by dividing 56 by 4, which gives us 19. Subtracting 5 from 19 gives us our answer of 14 feet.
Answer:
![\boxed{x = 4}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%20%3D%204%7D)
Step-by-step explanation:
=> 5x-4+2(x-4) = 16
Expanding the brackets
=> 5x-4+2x-8 = 16
Combining like terms
=> 5x+2x-4-8 = 16
=> 7x - 12 = 16
Adding 12 to both sides
=> 7x = 16+12
=> 7x = 28
Dividing both sides by 7
=> x = 4
Answer:
LM+MN=LN
3x-5+x+7=17
4x=17+5-7
4x=15
x=15/4=3.75
LM= 3x-5=3*3.75-5=6.25
Step-by-step explanation:
Answer:
lmk if u ended up with a retake or sum sorry nobody got bk to before it was due