Answer:
There are two ways to do this problem algebraically or trigonometrically.
Algebraically/geometrically
The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.
The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3
Using Trig.
We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).
Therefore, sin(pi/3) = 6/r =
r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3
Lol ok where’s the question is this just for fun?
The simultaneous equations are
2x - 7y = 4 (1)
3x + y = -17 (2)
Write (2) as
y = - 3x - 17 (3)
Substitute (3) into (1).
2x - 7(-3x - 17) = 4
2x + 21x + 119 = 4
23x = -115
x = -5
This is the equation obtained after substituting y from the second equation into the first equation.
The solution for y is
y = -3(-5) - 17 = -2
Answer: x = -5
Note: The solution is x = -5, y = -2.
