Question

If I know the lengths of two sides of a right triangle, how do I find the third?
Could I find the two missing side lengths of a right triangle if I only know one side length and one angle measure (other than the 90 degree angle)?
Could I find the two missing angle measures if I know some of the side lengths of a right triangle?
What makes a triangle a “special” right triangle? How can special right triangles help me find side lengths?

Answer 1

Random question <.< did you attend University High in Orange City Florida?

Answer 2

Finding the missing side of a right triangle is a pretty simple matter if two sides are known. One of the more famous mathematical formulas is a2 + b2 = c2, which is known as the Pythagorean Theorem. The theorem states that the hypotenuse of a right triangle can be easily calculated from the lengths of the sides. The hypotenuse is the longest side of a right triangle.

Right Triangle

If you're given the lengths of the two sides it is easy to find the hypotenuse. Just square the sides, add them, and then take the square root. Here's an example:

Sample Triangle

Since we are given that the two legs of the triangle are 3 and 4, plug those into the Pythagorean equation and solve for the hypotenuse:

a2 + b2 = c2

32 + 4 2 = c2

9 + 16 = c2

c = 5

If you are given the hypotenuse and one of the legs it's going to be slightly more complicated, but only because you have to do some algebra first. Suppose you know that one leg is 5 and the hypotenuse (longest side) is 13. Plug those into the appropriate places in the Pythagorean equation:

a2 + b2 = c2

52 + b2 = 13 2

25 + b2 = 169

b2 = 144

b = 12

As you can see, it is pretty simple to use the Pythagorean Theorem to find the missing side length of a right triangle. But -- what if it's not a right triangle? If you change that angle in the triangle there can obviously be any number of possibilities for the hypotenuse! Thus, you need more information. You can try using the Law of Sines or the Law of Cosines to determine side lengths in other triangles.


Here's an example from a site I use