Equilateral Triangles

A2+B2 = C2
BB-41-B- Find the height of an equilateral triangle with sides of 6.

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal 60 degrees angles.

The three angles of the triangle add up together equal 180o. As in the picture above each angle is 60o. And there are 3 sides so 3*60= 180o. The sides on equilateral triangles are all the same side as shown in the picture above. However if it were an isosceles triangle two sides would be the same and one would be different. However on a right triangle all the sides would be different with an angle of 90o.

90o

To answer this problem FX-41b finding the height of an equilateral triangle with sides of 6.

In order to find the length of the height of the triangle you need to use the Pythagorean Theorem, which is A2+B2 =C2.When we use the Pythagorean Theorem we use half of the triangle so the bottom is cut into half. So instead of the length of 6 on the bottom it is 3. This is a given number. And we want to find the height so we use the hypotenuse as another given number, which is 6. So now we plug these to numbers in the equation A2+B2 = C2. 6 is the hypotenuse so we substitute it for c2 and the 3 can be substituted for the A or B. In this case we used 3 to substitute the A and the height “would be the b and we substitute the b for the h. So the equation would be 32+h2=62. Then you square the 3 and the 6 so the next equation would be 9+h2=36. After that you subtract the 9 from both sides of the equation which would be h2=27. Next you solve for h which would be h=3√3≈5.2

32+h2=62
9 +h2=36
-9 -9
h2=27
h=3√3≈5.2
So the height of the triangle is ≈5.2.