Question

A triangle has side lengths 4 ft, 12 ft, and 13 ft. Is the triangle acute, obtuse, or right?

Show work

Answer obtuse

Answer 1

To determine if the triangle is acute, obtuse or right, we need to identify the largest side of the triangle.

In this case, the largest side of the triangle is 13 ft.

Now, we need to check if the sum of the squares of the two smaller sides is greater than, less than, or equal to the square of the largest side.

That is, if 4^2 + 12^2 < 13^2, then the triangle is obtuse; if 4^2 + 12^2 > 13^2, then the triangle is acute; and if 4^2 + 12^2 = 13^2, then the triangle is right.

Simplifying the equation, we get:

16 + 144 < 169

160 < 169

Since 160 is less than 169, we can see that the sum of the squares of the two smaller sides is less than the square of the largest side.

Therefore, the triangle is obtuse.