Answer: ![\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}](https://tex.z-dn.net/?f=%5Cbold%7B5%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Csqrt%7B11%7D%7D%7B6%7D%5Cqquad%206%29%5C%20%5Ctan%20%5Ctheta%20%3D%5Cdfrac%7B8%7D%7B17%7D%5Cqquad%207%29%5C%20%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%208%29%5C%20%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Csqrt%7B10%7D%7D%7B10%7D%7D)
<u>Step-by-Step Explanation:</u>
Pythagorean Theorem is: a² + b² = c² , <em>where "c" is the hypotenuse</em>
![5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}](https://tex.z-dn.net/?f=5%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bhypotenuse%20of%20triangle%7D%7D%3D%5Cdfrac%7B3%5Csqrt%7B11%7D%7D%7B18%7D%5Cquad%20%5Crightarrow%20%5Clarge%5Cboxed%7B%5Cdfrac%7B%5Csqrt%7B11%7D%7D%7B6%7D%7D)
Note: (15)² + (3√11)² = hypotenuse² → hypotenuse = 18
![6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}](https://tex.z-dn.net/?f=6%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bhypotenuse%20of%20triangle%7D%7D%3D%5Cdfrac%7B8%7D%7B17%7D%5Cquad%20%3D%5Clarge%5Cboxed%7B%5Cdfrac%7B8%7D%7B17%7D%7D)
Note: 8² + 15² = hypotenuse² → hypotenuse = 17
![7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}](https://tex.z-dn.net/?f=7%29%5C%20%5Ctan%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20opposite%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%3D%5Cdfrac%7B20%7D%7B15%7D%5Cquad%20%5Crightarrow%20%5Clarge%5Cboxed%7B%5Cdfrac%7B4%7D%7B3%7D%7D)
Note: hypotenuse not needed for tan
![8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}](https://tex.z-dn.net/?f=8%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bhypotenuse%20of%20triangle%7D%7D%3D%5Cdfrac%7B2%7D%7B2%5Csqrt%7B10%7D%7D%5Cquad%20%3D%5Clarge%5Cboxed%7B%5Cdfrac%7B%5Csqrt%7B10%7D%7D%7B10%7D%7D)
Note: 2² + 6² = hypotenuse² → hypotenuse = 2√10
Answer:
x = 23.78
.........................
27.1739% percent. to find that, all you have to do is multiply 2.5x100. that equals 250. divide this by 9.2, and that is your answer
Answer:
18
Step-by-step explanation:
Since you know the perimeters are equal, write your equation.
x+6 + x+6 + x+6 = x + x+6 + 2x-6
combine like terms
3x + 18 = 4x
isolate your x by subtracting 3x from each side
18 = x
check your answer:
3x + 18 = 72
4x = 72