By Pythagorean theorem,
a^2+b^2=c^2
c is the longest side of the triangle
a and b are the remaining sides
Given:
In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°.
To find:
The all possible values of ∠X, to the nearest degree.
Solution:
Law of Sines:
![\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%7D%7B%5Csin%20A%7D%3D%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%3D%5Cdfrac%7Bc%7D%7B%5Csin%20C%7D)
For ΔWXY,
![\dfrac{w}{\sin W}=\dfrac{x}{\sin X}=\dfrac{y}{\sin Y}](https://tex.z-dn.net/?f=%5Cdfrac%7Bw%7D%7B%5Csin%20W%7D%3D%5Cdfrac%7Bx%7D%7B%5Csin%20X%7D%3D%5Cdfrac%7By%7D%7B%5Csin%20Y%7D)
Now,
![\dfrac{w}{\sin W}=\dfrac{x}{\sin X}](https://tex.z-dn.net/?f=%5Cdfrac%7Bw%7D%7B%5Csin%20W%7D%3D%5Cdfrac%7Bx%7D%7B%5Csin%20X%7D)
![\dfrac{900}{\sin (157^\circ)}=\dfrac{680}{\sin X}](https://tex.z-dn.net/?f=%5Cdfrac%7B900%7D%7B%5Csin%20%28157%5E%5Ccirc%29%7D%3D%5Cdfrac%7B680%7D%7B%5Csin%20X%7D)
![900\sin X=680\sin (157^\circ)](https://tex.z-dn.net/?f=900%5Csin%20X%3D680%5Csin%20%28157%5E%5Ccirc%29)
![\sin X=\dfrac{680}{900}\sin (157^\circ)](https://tex.z-dn.net/?f=%5Csin%20X%3D%5Cdfrac%7B680%7D%7B900%7D%5Csin%20%28157%5E%5Ccirc%29)
![\sin X=0.295219](https://tex.z-dn.net/?f=%5Csin%20X%3D0.295219)
![X=\sin^{-1}(0.295219)](https://tex.z-dn.net/?f=X%3D%5Csin%5E%7B-1%7D%280.295219%29)
![X=17.17067](https://tex.z-dn.net/?f=X%3D17.17067)
![X\approx 17](https://tex.z-dn.net/?f=X%5Capprox%2017)
Therefore, the value of ∠X is 17 degrees.
Answer:
the answer for the volume of the cylinder is V≈25.13in³
Answer: x=14
Step-by-step explanation:
The angles in a triangle are equal to 180 so
6x + 3 + 5x + x + 9 = 180
12x + 12 = 180
-12 -12
12x = 168
x = 14