Hello,
This is an example that utilizes the Pythagorean Theorem.
In this question, you asked to determine the lengths of the sides of the tringle. Notice the sides of the triangle (not including the hypotenuse) consist of a vertical and horizontal line. That means for 1 line, the y coordinate remains the same, while for the other, the x coordinate remains the same. If you look at the height of the triangle, you can see that the line is vertical with the top point having an x coordinate of 3, indicating that the x coordinate of the vertex of the 90 degree angle is also 3.
The same applies for the base of the triangle, except the line is horizontal so the y coordinate remains the same as the given point on the left vertex of the triangle. So, we know the y coordinate of the vertex of the 90 degree angle is also -4.
So, we know the coordinates of the vertex of the 90 degree angle is (3, -4)
Now we can find the distance from each other given point of the triangle to the 90 degree angle vertex.
The distance from (3,2) to (3,-4) is 6.
The distance from (-2,-4) to (3,-4) is 5.
So, we know the two sides of a right triangle are 5 and 6.
Using the pythagorean theorem, [tex] 5^{2} + 6^{2} = 61
[/tex]
So the length of the hypotenuse is [tex] \sqrt{61} = 7.81[/tex]
The lengths of the sides of the triangle are 6 (height) and 5 (base). The length of the hypotenuse is around 7.81.
Hope this helps!
