Answer:
θ = 0.9626
Step-by-step explanation:
Hi there!
We're given the hypotenuse and the leg adjacent to θ in this right triangle. To find θ, we can use the cosine ratio:
![\displaystyle cos\theta=\frac{adjacent}{hypotenuse}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%3D%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D)
Plug in the given information
![\displaystyle cos\theta=\frac{4}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Ctheta%3D%5Cfrac%7B4%7D%7B7%7D)
Use the inverse cosine ratio
![\displaystyle \theta=cos^-^1(\frac{4}{7})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%3Dcos%5E-%5E1%28%5Cfrac%7B4%7D%7B7%7D%29)
Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)
![\displaystyle \theta=0.9626](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%3D0.9626)
Therefore, θ = 0.9626 when rounded to four decimal places.
I hope this helps!
Answer: Length = 10cm
Width = 6.5cm
Step-by-step explanation:
Let the width of the rectangle be represented by x.
Therefore, the length of the rectangle will be: = (2 × x) - 3 = 2x - 3
Therefore area of a rectangle = length × width
x(2x - 3) = 65
2x² - 3x = 65
2x² - 3x - 65 = 0
2x² + 10x - 13x - 65 = 0
2x(x + 5) - 13(x + 5) = 0
(2x - 13)(x + 5) = 0
2x - 13 = 0
2x = 13
x = 13/2
x = 6.5
Width = 6.5cm
Length = 2x - 3
= 2(6.5) - 3
= 13 - 3
= 10cm
Therefore, the length of the rectangle is 10cm and the width is 6.5cm.
X + 9 = -12
x + 9 - 9 = -12 -9
x = -12 -9
x = -1(12+9)
x= -1(21)
x = -21