Answer:
Approximatley 5.8 units.
Step-by-step explanation:
We are given two angles, ∠S and ∠T, and the side opposite to ∠T. We need to find the unknown side opposite to ∠S. Therefore, we can use the Law of Sines. The Law of Sines states that:
![\frac{\sin(A)}{a}=\frac{\sin(B)}{b} =\frac{\sin(C)}{c}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%28A%29%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%28B%29%7D%7Bb%7D%20%3D%5Cfrac%7B%5Csin%28C%29%7D%7Bc%7D)
Replacing them with the respective variables, we have:
![\frac{\sin(S)}{s} =\frac{\sin(T)}{t} =\frac{\sin(R)}{r}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%28S%29%7D%7Bs%7D%20%3D%5Cfrac%7B%5Csin%28T%29%7D%7Bt%7D%20%3D%5Cfrac%7B%5Csin%28R%29%7D%7Br%7D)
Plug in what we know. 20° for ∠S, 17° for ∠T, and 5 for <em>t</em>. Ignore the third term:
![\frac{\sin(20)}{s}=\frac{\\sin(17)}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%2820%29%7D%7Bs%7D%3D%5Cfrac%7B%5C%5Csin%2817%29%7D%7B5%7D)
Solve for <em>s</em>, the unknown side. Cross multiply:
![\frac{\sin(20)}{s}=\frac{\sin(17)}{5}\\5\sin(20)=s\sin(17)\\s=\frac{5\sin(20)}{\sin(17)} \\s\approx5.8491\approx5.8](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%2820%29%7D%7Bs%7D%3D%5Cfrac%7B%5Csin%2817%29%7D%7B5%7D%5C%5C5%5Csin%2820%29%3Ds%5Csin%2817%29%5C%5Cs%3D%5Cfrac%7B5%5Csin%2820%29%7D%7B%5Csin%2817%29%7D%20%5C%5Cs%5Capprox5.8491%5Capprox5.8)
Answer:
put the data in ascending order
not sure if it's correct
Answer:
193 in
Step-by-step explanation:
Volume of a triangular prism:
The volume of a triangular prism is the base area multiplied by the wedge, that is:
![V = A_bw](https://tex.z-dn.net/?f=V%20%3D%20A_bw)
The base area is one half times the triangle base times it's height, so:
![V = 0.5*b*h*w](https://tex.z-dn.net/?f=V%20%3D%200.5%2Ab%2Ah%2Aw)
The wedge of cheese is 7 inches tall.
This means that ![w = 7](https://tex.z-dn.net/?f=w%20%3D%207)
The base of the cheese is shaped like a triangle with a base of 11 and a height of 5 inches.
This means that ![b = 11, h = 5](https://tex.z-dn.net/?f=b%20%3D%2011%2C%20h%20%3D%205)
Volume:
![V = 0.5*b*h*w = 0.5*11*5*7 = 192.5](https://tex.z-dn.net/?f=V%20%3D%200.5%2Ab%2Ah%2Aw%20%3D%200.5%2A11%2A5%2A7%20%3D%20192.5)
Rounding, approximately 193 in.