You can solve for sides of a triangle using the following equation.
A = arccos (b^2 + c^2 - a^2/2bc)
And likewise for other variables by moving the letters.
Ultimately, in this problem you get the following angle measures:
15.87
23.97
140.16
I think the answer is 60 and 30 but I'm on break so I'm not thinking rn
Answer:
All potential roots are 3,3 and
.
Step-by-step explanation:
Potential roots of the polynomial is all possible roots of f(x).
![f(x)=3x^3-13x^2-3x+45](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3-13x%5E2-3x%2B45)
Using rational root theorem test. We will find all the possible or potential roots of the polynomial.
p=All the positive/negative factors of 45
q=All the positive/negative factors of 3
![p=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45](https://tex.z-dn.net/?f=p%3D%5Cpm%201%2C%5Cpm%203%2C%5Cpm%205%5Cpm%20%5Cpm%209%2C%5Cpm%2015%5Cpm%2045)
![q=\pm 1,\pm 3](https://tex.z-dn.net/?f=q%3D%5Cpm%201%2C%5Cpm%203)
All possible roots
![\frac{p}{q}=\pm 1,\pm 3,\pm 5\pm \pm 9,\pm 15\pm 45,\pm \frac{1}{3},\pm \frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7Bq%7D%3D%5Cpm%201%2C%5Cpm%203%2C%5Cpm%205%5Cpm%20%5Cpm%209%2C%5Cpm%2015%5Cpm%2045%2C%5Cpm%20%5Cfrac%7B1%7D%7B3%7D%2C%5Cpm%20%5Cfrac%7B5%7D%7B3%7D)
Now we check each rational root and see which are possible roots for given function.
![f(1)= 3\times 1^3-13\times 1^2-3\times 1+45\Rightarrow 32\neq 0](https://tex.z-dn.net/?f=f%281%29%3D%203%5Ctimes%201%5E3-13%5Ctimes%201%5E2-3%5Ctimes%201%2B45%5CRightarrow%2032%5Cneq%200)
![f(-1)= 3\times (-1)^3-13\times (-1)^2-3\times (-1)+45\Rightarrow \neq 32](https://tex.z-dn.net/?f=f%28-1%29%3D%203%5Ctimes%20%28-1%29%5E3-13%5Ctimes%20%28-1%29%5E2-3%5Ctimes%20%28-1%29%2B45%5CRightarrow%20%5Cneq%2032)
![f(-3)= 3\times (-3)^3-13\times (-3)^2-3\times (-3)+45\Rightarrow \neq -144](https://tex.z-dn.net/?f=f%28-3%29%3D%203%5Ctimes%20%28-3%29%5E3-13%5Ctimes%20%28-3%29%5E2-3%5Ctimes%20%28-3%29%2B45%5CRightarrow%20%5Cneq%20-144)
![f(3)= 3\times (3)^3-13\times (3)^2-3\times (3)+45\Rightarrow =0\\\\ \therefore x=3\text{ Potential roots of function}](https://tex.z-dn.net/?f=f%283%29%3D%203%5Ctimes%20%283%29%5E3-13%5Ctimes%20%283%29%5E2-3%5Ctimes%20%283%29%2B45%5CRightarrow%20%3D0%5C%5C%5C%5C%20%5Ctherefore%20x%3D3%5Ctext%7B%20Potential%20roots%20of%20function%7D)
Similarly, we will check for all value of p/q and we get
![f(-5/3)=0](https://tex.z-dn.net/?f=f%28-5%2F3%29%3D0)
Thus, All potential roots are 3,3 and
.