We are given the following right triangle with side lengths a, b, and c. We are asked to describe how we can solve the triangle when side lengths a or b are missing.
Note that no matter what side is missing, we can always use the Pythagorean Theorem. This theorem tells us about the relationship between the legs of the triangle 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.
Since our trianlge is right, we can also write this theorem using symbols.
Now, let's consider each of the two cases.
Lengths b and c Are Known
Picture this: we are given the lengths b and c. We want to find a. To do so, we can use the equation we wrote earlier.
a^2+b^2=c^2
First, we substitute the known values of b and c into the equation. Next we solve for the missing length a. To better see how this works, let b=12 and c=13. We are going to find a.
There are two solutions to the equation, a=- 5 and c=5. Because a length cannot be negative, a=5 is our solution.
Lengths b and c Are Known
This time we are given the lengths a and b. We want to find c. To do so, we should once again use the Pythagorean Theorem.
a^2+b^2=c^2
We substitute the known values, in this case a and b, into the equation. Next we solve for the missing length c. Let's take a look at an example. We will use a=6 and b=8 to find c.
