From: Glynnis

I am taking Fundamentals of Math in College and I'm having a hard time figuring out how you find the measure of a side that is not the hypotenuse, using the Pythagorean Theorem?  Also, how do you figure the surface area abd volume of a cone when the radius is 5 yards and the height is 8 yards?

Hi Glynnis.

The Pythagorean Theorem is for right-triangles (that is, a triangle where one angle is 90 degrees).
Pythagorean Theorem: c² = a² + b²

where c is the length of the hypotenuse and a and b are the other two sides. So you can see from this that there are three variables. If you know any two, you can use the Pythagorean Theorem to find the third - just plug in the values you do know and solve for the unknown variable. If you are not working with a right triangle, then you need a different formula and more information. The Law of Cosines lets you figure out the length of the side of any triangle if you know the lengths of the other two sides and the angle between those two sides you know.
Law of Cosines: c² = a² + b² - 2abcosC

where C is the angle I mentioned.

The second question you asked is the same as this earlier question. Take a look at what Walter wrote to learn how to figure out a cone's surface area. The volume of a cone is given by the formula V = ^π /₃ r² h.

Hope this helps!
Stephen La Rocque.