Question

Determine if a triangle with side lengths 8, 14, and 15 is acute, right, or obtuse

Answer 1

Answer:

Acute

Step-by-step explanation:

The Converse of the Pythagorean Theorem states that:

• If $a^2+b^2 > c^2$ then the triangle is acute.
• If $a^2+b^2 < c^2$ then the triangle is obtuse.
• If $a^2+b^2 = c^2$ then the triangle is right.

The side lengths 8, 14, and 15 are given. We can assume the hypotenuse (or c) is the longest side length, so it is 15.

• c = 15

It doesn't matter which order of the numbers are plugged in for a and b, so a and b will be 8 and 14.

• a = 8
• b = 14

Now we have to add $a^2$ and $b^2$ to see if the sum is greater than, less than, or equal to 15 (c).

• $a^2 + b^2$
• $8^2 + 14^2$

Calculate the rest of the problem.

• $8^2=64 \newline 14^2=196$

• $64+196=260$

We have to find what $15^2$ is before we can make a decision using the Converse of the Pythagorean Theorem.

• $15^2=225$

260 ($a^2+b^2$) is greater than 225 ($c^2$). This means that the triangle is acute because $a^2+b^2>c^2$.