SOLUTION: Triangle ABC is an equilateral triangle. BC=10 What is the length of Ab? LINK TO TRIANGLE http://www.calculatorsoup.com/images/triangle-equilateral-001.gif

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Question 472745: Triangle ABC is an equilateral triangle.
BC=10
What is the length of Ab?
LINK TO TRIANGLE
http://www.calculatorsoup.com/images/triangle-equilateral-001.gif
Found 2 solutions by Theo, MathLover1:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Since it's an equilateral triangle, then all sides are equal to 10.
This means that:
AB = 10
AC = 10
BC = 10
Since it's an equilateral triangle, then the altitude is perpendicular to the base and is also the median to the base which means that it splits the base in half.
This means that Ab is equal to 5.
Since it's an equilateral triangle, than all angles are equal.
This means that angle:
A = 60 degrees
B = 60 degrees
C = 60 degrees
Since it's an equilateral triangle, this means that the altitude to the triangle also bisects angle B.
This means that angle ABb is equal to 30 degrees.
Since you know that AB is equal to 10 and angle ABb is equal to 30 degrees, then you can find the length of Ab by using the sine of ABb.
Sine (ABb) = opposite / hypotenuse = x / 10
Since ABb) is equal to 30 degrees, this formula becomes:
Sine (30) = x/10
multiply both sides of this equation by 10 to get:
10 * Sine(30) = x
solve for x to get:
x = 10 * (1/2) = 5.
You get the same answer a couple of ways, as you should.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
BC=10
Triangle ABC is an equilateral triangle; so AB=BC=10