Question

The sides of a triangle are 30, 64, and 90. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.

Answer 1

the triangle is obtuse

Explanation:

`{90}^(2) = 8100`

`{30}^(2) + {64}^(2) = 4996`

`{30}^(2) + {60}^(2) < {90}^(2)`

triangle is obtuse because the square of the largest is greater than the sum of the square of the other 2 sides

Answer 2

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's check if the triangle with sides of 30, 64, and 90 is a right triangle:

30^2 + 64^2 = 900 + 4096 = 4996

90^2 = 8100

Since 4996 is less than 8100, the triangle is not a right triangle.

In an acute triangle, all angles are less than 90 degrees. In an obtuse triangle, one angle is greater than 90 degrees.

To determine if the triangle is acute or obtuse, we need to find the largest side. The largest side is 90. Let's find the sum of the squares of the other two sides:

30^2 + 64^2 = 900 + 4096 = 4996

Since 4996 is less than 90^2, the triangle is acute.

Therefore, the triangle with sides of 30, 64, and 90 is an acute triangle.