How To Find The Missing Side Length Of A Triangle

Employ the Pythagorean Theorem for Correct Triangles...

Question:

If I'm given a right triangle and ii of its sides, how can I observe the length of the third side? Tin can I practise this if it'due south not a correct triangle?

Answer

Finding the missing side of a right triangle is a pretty elementary matter if 2 sides are known. I of the more than famous mathematical formulas is $a^ii+b^two=c^2$, which is known equally the Pythagorean Theorem. The theorem states that the hypotenuse of a right triangle can be hands calculated from the lengths of the sides. The hypotenuse is the longest side of a correct triangle.

Right Triangle

If yous're given the lengths of the two sides it is easy to notice the hypotenuse. Just square the sides, add them, and and so take the foursquare root. Here's an case:

Sample Triangle

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

$$ a^two+b^2=c^2 $$ $$ iii^2+4^ii=c^ii $$ $$ 25 = c^2 $$ $$ c = \sqrt{25} $$ $$ c = 5 $$

If y'all are given the hypotenuse and one of the legs, it'due south going to be slightly more than complicated, merely only because y'all accept to do some algebra first. Suppose you know that 1 leg is v and the hypotenuse (longest side) is thirteen. Plug those into the appropriate places in the Pythagorean equation:

$$ a^2+b^2=c^two $$ $$ 5^two+b^ii=13^2 $$ $$ 25+b^2=169 $$ $$ b^ii=144 $$ $$ b = 12 $$

As you tin run across, it is pretty simple to apply the Pythagorean Theorem to discover the missing side length of a right triangle. Only -- what if it's not a right triangle? If yous change that angle in the triangle in that location can apparently be whatsoever number of possibilities for the hypotenuse! Thus, you lot need more than information to solve the trouble. You lot can endeavour using the Law of Sines or the Constabulary of Cosines to determine side lengths in other triangles.