Answer:
16
Step-by-step explanation:
Answer:
_ is equal to 28
Step-by-step explanation:
numerator is multiplied by 4, therefore, due to the equal sign, the denominator must also by multiplied by 4
Solution:
Given:
A circle with the sector details;
![\begin{gathered} r=19\text{ }in \\ \theta=135^0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20r%3D19%5Ctext%7B%20%7Din%20%5C%5C%20%5Ctheta%3D135%5E0%20%5Cend%7Bgathered%7D)
The area of a sector is given by;
![\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ A=\frac{135}{360}\times\pi\times19^2 \\ A=\frac{1083\pi}{8}\text{ }in^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Ctimes%5Cpi%20r%5E2%20%5C%5C%20A%3D%5Cfrac%7B135%7D%7B360%7D%5Ctimes%5Cpi%5Ctimes19%5E2%20%5C%5C%20A%3D%5Cfrac%7B1083%5Cpi%7D%7B8%7D%5Ctext%7B%20%7Din%5E2%20%5Cend%7Bgathered%7D)
Therefore, the area of the sector is;
SinB = 8/17
The sin of an angle is equal to opposite/hypotenuse
Use Pythagorean’s Theorem to solve for the opposite side
![15^{2} +b^{2}=17^{2} \\225 + b^{2} =289\\b^{2} =64\\b=8](https://tex.z-dn.net/?f=15%5E%7B2%7D%20%2Bb%5E%7B2%7D%3D17%5E%7B2%7D%20%20%5C%5C225%20%2B%20b%5E%7B2%7D%20%3D289%5C%5Cb%5E%7B2%7D%20%3D64%5C%5Cb%3D8)
The opposite side is equal to 8
So sinB = 8/17
*look at attached photo for work
-0.65625 or -21/32 should be your answer just cross multiply