Hi!
Rules for solving 30-60-90 triangles are as follows:
* The hypotenuse is double the short leg.
* The short leg times √3 is the long leg
To solve then, we divide 4√21 by √3 and get 4√7. That is x, and to get y we multiply by 2. That is 8√7.
Hope this helps! :D
If you expand the square, you have
Simplify the right hand side:
Cancel the -3x appearing on both sides:
Multiply both sides by 4:
Consider the square root of both terms (using the doubles sign):
Answer:
z = -12
Step-by-step explanation:
The given system of equations is:
xy/(x + y) = 1 ...........................(1)
xz/(x + z) = 2...........................(2)
yz/(y + z) = 3...........................(3)
From (1): x + y = xy
=> y = xy - x
y = x(y - 1)
x = y/(y - 1).......................................(4)
From (2): 2(x + z) = xz
=> 2x + 2z = xz
2x = xz - 2z
2x = z(x - 2)
z = 2x/(x - 2) ....................................(5)
From (3): 3(y + z) = yz
=> 3y + 3z = yz
3y = yz - 3z
3y = z(y - 3)
z = 3y/(y - 3)....................................(6)
Comparing (5) and (6)
2x/(x - 2) = 3y/(y - 3)
2x(y - 3) = 3y(x - 2)
2xy - 6x = 3xy - 6y
6(y - x) = xy .................................(7)
But from (1): xy = x + y
Using this in (7), we have
6(y - x) = x + y
6y - y - 6x - x = 0
5y - 7x = 0
5y = 7x
x = 5y/7................................................(8)
Using this in (4)
5y/7 = y/(y - 1)
1/(y - 1) = 5/7
(y - 1) = 7/5
y = 1 + 7/5
y = 12/5..........................................(9)
Using this in (8)
x = 5(12/5)/7 = 12/7 .......................(10)
Using (10) in (5)
z = 2x/(x - 2)
z = 2(12/7) ÷ (12/7 - 2)
= 24/7 ÷ -2/7
= 24/7 × (-7/2)
= -24/2 = -12
z = -12.
Let’s says that x is the measure of the angle. X and it’s supplement are equal to 180. X and it’s complement are equal to 90. The supplement is s and the complement is c. S is times c which is the same as 3c.
3c + x = 180
C+x = 90
X = 90 - c
3c + 90 - c = 180
2c = 90
C = 45
The complement of. 45 degree angle is 45 degrees.
The angle is 45 degrees.
