Given:
In ΔABC, AB = 5 unit, BC = 2 unit and ∠C = 90°
To find the The value of ∠B.
Formula
By Trigonometric Ratio we know,
![cos \ \theta=\frac{adj}{hyp}](https://tex.z-dn.net/?f=cos%20%5C%20%5Ctheta%3D%5Cfrac%7Badj%7D%7Bhyp%7D)
Let us take ∠B = θ
With respect to θ, BC is the adjacent side and AB is the hypotenuse.
So,
![cos \ \theta=\frac{BC}{AB}](https://tex.z-dn.net/?f=cos%20%5C%20%5Ctheta%3D%5Cfrac%7BBC%7D%7BAB%7D)
![cos \ B=\frac{2}{5}](https://tex.z-dn.net/?f=cos%20%5C%20B%3D%5Cfrac%7B2%7D%7B5%7D)
![B=cos^{-1} (\frac{2}{5} )](https://tex.z-dn.net/?f=B%3Dcos%5E%7B-1%7D%20%28%5Cfrac%7B2%7D%7B5%7D%20%29)
![B = 66.42^{\circ}](https://tex.z-dn.net/?f=B%20%3D%2066.42%5E%7B%5Ccirc%7D)
Hence, the value of ∠B is 66.42°.
To calculate the distance between two points, we can use a formula that is a variation Pythagorean Theorem. Look:
![\mathsf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}](https://tex.z-dn.net/?f=%5Cmathsf%7Bd%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%7D)
"d" represents the distance and coordinates are expressed as follows: (x, y)
Let's go to the calculations.
The answer is 8.06 uc.
From the picture attached, you can see that:
A'(-3, -1)
B'(-1, -8)
C'(-7, -2)
Therefore, the transformation is:
x' = -x
y' = -y
These functions represent a rotation of 180° about the origin.
Therefore ΔABC is
rotated counterclockwise 180° about the origin to form ΔA'B'C'.
Given the function f(x) and f(g), the composite result function f(g(x)) is 3x - 16.
<h3>What is the composite result function f(g(x))?</h3>
Given the functions in the question;
- f(x) = 3x + 5
- g(x) = x - 7
- f(g(x)) = ?
To determine f(g(x)), we set up the result of the function.
f(g(x)) = f( x - 7 )
f(x) = 3x + 5
We replace all occurrence of x with x-7 and simplify
f( x - 7 ) = 3( x - 7 ) + 5
f( x - 7 ) = 3x - 21 + 5
f( x - 7 ) = 3x - 16
Given the function f(x) and f(g), the composite result function f(g(x)) is 3x - 16.
Learn more about composite function here: brainly.com/question/20379727
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