Question

Classify the triangle with sides 6, 8, 15 (Not obtuse).

a) acute
b) right
c) not a triangle
d) cannot be determined from the information given

Answer 1

The triangle with sides 6, 8, 15 is classified as acute.

Step-by-step explanation:

To classify the triangle with sides 6, 8, 15, we need to determine if it is acute, right, or not a triangle. According to the Pythagorean theorem, for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Let's check if this condition is satisfied:

6^2 + 8^2 = 36 + 64 = 100

15^2 = 225

Since 100 is not equal to 225, the triangle is not a right triangle. Now, since all the angles of the triangle must be less than 90 degrees for it to be acute, and since it is not a right triangle, the triangle must be obtuse. Therefore, the correct answer is (a) acute.