Geometry Homework

Question

Create a Pythagorean Theorem equation for the following information about a triangle, then solve for the unknown side. Side A = 9, side b = 6.

Answer 1

There are two possible answers here depending of which side is the hypotenuse. (That is, which side is the longest and is across from the right angle.) You should be able to tell this by looking at the diagram on your homework.

Since the hypotenuse is the longest side, it can't be b=6. It could be a=9, or it could be c=?

First let's assume the hypotenuse is c. We then get the equation:

a² + b² = c²

Plugging in for a and b, we get:

9² + 6² = c²

81 + 36 = c²

117 = c²

c = √117

c ≈ 10.816

If instead, a is the hypotenuse, we get the following equation:

b² + c² = a²

Then we substitute for a and b and solve, like before. (Except this time our answer should be less than 9):

6² + c² = 9²

36 + c² = 81

c² = 45

c = √45

c = 3√5

c ≈ 6.708