How do I find the altitude of a triangle?

Question

I'm so confused! The sides of an equilateral triangle are 12 cm. How do I find the altitude? The sides of a right triangle are 5,12, and 13. How do I find the altitude? An isosceles triangle has sides the measures 13, 13, and 10. HOW DO I FIND THE ALTITUDE? I have mid-terms on Tuesday, so I need to know. I'm very appreciative of anyone's help.

Answer 1

Use the Pythagorean Theorem. In the equilateral triangle, if you (in your mind or on paper) drop a perpendicular from the apex to the base, it will hit it in the middle and make two right-angled triangles. So the sides you know are 12 cm, half of 12 or 6 cm, and the altitude (the perpendicular line). Pythagoras says that 12^2 = 6^2 + A^2, so A^2 = 144 - 36 = 108. A would be the square root of 108, or just over 10 cm.
Use a calculator.

In a right triangle, it depends how you orient it on the paper. If you use the 12cm side as the base, then the 5cm side is the altitude, because it's at 90 degrees to the base. Or vice-versa.

The 13,13,10 triangle is isoceles. Use the 10 as the base, and follow the same directions as for the equilateral triangle. The sides of each half, would be 13, 5 (half the original base) and the altitude you want. A^2 = 13^2 - 5^2 = 169 - 25 = 144. So the altitude is the square root of this, or 12. (Each half triangle is the same as the second triangle you worked on.)

Answer 2

One at a time. In an equilateral triangle, if you drop a perpendicular from the top point to the middle of the base, you can use Pythagoras to measure that line, which will, of course, be the altitude.
If the sides of a right triangle are 5, 12, and 13, either the 5-side or the 12-side can be taken as the base, and the other one is the altitude.
On the isosceles triangle, draw a perpendicular to the 10-side from the opposite angle. (This line will be the altitude.) It will bisect the 10-side into two triangles of base 5, and since the hypotenuse is 13, the altitude will be 12.

Answer 3

the altitude is a line the starts at the vertex of the triangle and intersects the other line forming a right angle. hope this helps