What's the question- what is x?
So for this triangle, since it's not right (No 90° angle, at least not shown), we must use special trigonometric triangles. You may have used Pythagorean Theorem, but you can't unless it's a right triangle.
Now we decide between Law of Sines vs. Law of Cosines. L. of Sines is for when we have 2 angles and one or more sides. L. of Cosines is for when we don't have that 2nd angle, but do have 2 sides... our case here.
Here's how the Law of Cosines works:
![{c}^{2} \: = {a}^{2} + {b}^{2} - (2ab \cos( \gamma )) \\ c = \sqrt{{a}^{2} + {b}^{2} - 2ab \cos( \gamma )}](https://tex.z-dn.net/?f=%7Bc%7D%5E%7B2%7D%20%20%5C%3A%20%20%3D%20%20%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20-%20%282ab%20%5Ccos%28%20%5Cgamma%20%29%29%20%5C%5C%20c%20%3D%20%20%5Csqrt%7B%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20%20-%202ab%20%5Ccos%28%20%5Cgamma%20%29%7D%20%20)
where c is the side needed, a & b are the 2 known sides, and gamma (γ) is the angle opposite the side c.
So a = 21, b = 42, γ = 39°
![c... \: \\ = \sqrt{{21}^{2} + {42}^{2} - 2(21)(42) \cos(39) }](https://tex.z-dn.net/?f=c...%20%5C%3A%20%20%20%5C%5C%20%3D%20%20%5Csqrt%7B%7B21%7D%5E%7B2%7D%20%20%2B%20%20%7B42%7D%5E%7B2%7D%20%20-%202%2821%29%2842%29%20%5Ccos%2839%29%20%20%7D%20)
![c = \sqrt{441 + 1764 - (1764 \cos(39)) }](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B441%20%2B%201764%20-%20%281764%20%5Ccos%2839%29%29%20%7D%20)
![c = \sqrt{2205 - (1764)(0.777)}](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B2205%20-%20%281764%29%280.777%29%7D%20)
![c = \sqrt{2205 - 1370.89} \\ c = \sqrt{834.11} = 28.88](https://tex.z-dn.net/?f=c%20%3D%20%5Csqrt%7B2205%20-%201370.89%7D%20%20%5C%5C%20c%20%3D%20%20%5Csqrt%7B834.11%7D%20%20%3D%2028.88)
NOPE YOU DID IT CORRECTLY!!
You're "x" = 28.88°
Answer: [20x, 8y] [9x, 16y]
Step-by-step explanation:
Go on x value 20 and go up to 8 on y value.
Go on x value 9 and go up 16 on y value.
Answer:
C) Quadrant III
Step-by-step explanation:
The coefficients corresponding to k = 0, 1, 2, ..., 5 in the
expansion of (x + y)^5 are 1, 5 , 10 , 10, 5, 1. The coefficients can be solve
using manual expansion of the term of using combination:
<span>nCr-1, where n is the power and r is the desired
therm,</span>