X = 10
The triangles are similar by SAS, so we can set up a proportion of their sides.
9/(33-9) = 12/(3x+2)
9/24 = 12/3x+2
Reduce
3/8 = 12/3x+2
Cross multiply
3(3x+2) = 12*8
Distribute and multiply
9x + 6 = 96
Subtract 6
9x = 90
Divide by 9
x = 10
Check:
9/24 = 12/3x+2
9/24 = 12/3*10 + 2
9/24 = 12/30 + 2
9/24 = 12/32
3/8 = 3/8 :)
66.6667%
Now we can see that our fraction is 66.666666666667/100, which means that 4:6 as a percentage is 66.6667%.
Answer: 9 centimeters
Step-by-step explanation:
Add up all the sides, 6 + 10 + 11 = 27,
Since it’s the perimeter of an equilateral triangle, you do
27 / 3 = 9, which is the answer.
Answer:
Step-by-step explanation:
Begin by squaring both sides to get rid of the radical. Doing that gives you:
Now use the Pythagorean identity that says
and make the replacement:
. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:
and then simplify to
Factor out the common cos(x) to get
and there you have your 2 trig equations:
cos(x) = 0 and 1 - cos(x) = 0
The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at
The second equation simplifies to
cos(x) = 1
Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.
So, in the end, your 3 solutions are
