We are asked to describe how we can solve a right triangle. Note that solving a right triangle means finding one of its missing lengths. To answer the question, let's take a look at a right triangle with side lengths a, b, and c.
Let's now remember the Pythagorean Theorem. This theorem tells us about the relationship between its legs a and b and the hypotenuse c.
Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We can also write this theorem using symbols.
We see that the values of a, b, and c are bonded by this equation. If one of the lengths is missing, we substitute the lengths of the other two sides into the equation to solve for the missing one. This is how we solve a right triangle.
Example
Here is a right triangle. In the graph we can see the lengths of its two legs.
We want to find the missing length of the hypotenuse c. For that, we will use the Pythagorean Theorem. Because the triangle is right, we can write the following equation.
6^2+8^2=c^2
Let's now solve the equation for c.
There are two solutions to the equation, c=- 10 and c=10. Because a length cannot be negative, c=10 is our solution. The length of the hypotenuse is 10 units.
