Finding Missing Length Of Triangle

Apply the Pythagorean Theorem for Right Triangles...

Question:

If I'm given a correct triangle and two of its sides, how can I find the length of the third side? Tin I practice this if it's non a right triangle?

Answer

Finding the missing side of a correct triangle is a pretty simple matter if two sides are known. Ane of the more famous mathematical formulas is $a^2+b^two=c^2$, which is known every bit the Pythagorean Theorem. The theorem states that the hypotenuse of a right triangle can exist 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 ii sides it is easy to detect the hypotenuse. Just square the sides, add together them, and so accept the foursquare root. Here's an example:

Sample Triangle

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

$$ a^2+b^ii=c^2 $$ $$ 3^2+iv^2=c^two $$ $$ 25 = c^2 $$ $$ c = \sqrt{25} $$ $$ c = 5 $$

If you are given the hypotenuse and one of the legs, it'southward going to be slightly more complicated, but simply considering you accept to practice some algebra beginning. Suppose you know that one leg is v and the hypotenuse (longest side) is 13. Plug those into the advisable places in the Pythagorean equation:

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

Every bit you can see, it is pretty simple to employ the Pythagorean Theorem to notice the missing side length of a right triangle. Simply -- what if it's not a right triangle? If you alter that angle in the triangle at that place can apparently exist whatever number of possibilities for the hypotenuse! Thus, you need more information to solve the problem. You can try using the Law of Sines or the Constabulary of Cosines to make up one's mind side lengths in other triangles.