Does a 6.5, 8, and 4.9 Triangle Have a Right Angle?

Introduction to Right Angle Triangles

A right angle triangle is a triangle that has one 90-degree angle. According to the Pythagorean Theorem, the square of the length of the hypotenuse (the side opposite the 90-degree angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be expressed as:

c2 a2 b2 where c is the hypotenuse, and a and b are the other two sides.

Verifying with 6.5, 8, and 4.9

Let's check if the sides 6.5, 8, and 4.9 form a right angle triangle using the Pythagorean Theorem:

Step-by-Step Verification

To determine if a triangle with sides 6.5, 8, and 4.9 is a right angle triangle, follow these steps:

Calculate: 82 6.52 4.92

Calculate:

82 64

6.52 42.25

4.92 24.01

Add the squares of the other two sides:

6.52 4.92 66.26

Compare the results:

64 ≠ 66.26

Since 82 ≠ 6.52 4.92, the triangle is not a right angle triangle.

Additional Verification

Another way to verify is to sort the sides in ascending order (4.9, 6.5, 8) and check if:

82 4.92 6.52

Calculate:

82 64

4.92 6.52 24.01 42.25 66.26

Again, 64 ≠ 66.26, confirming that the triangle is not a right angle triangle.

Conclusion

A triangle with sides 6.5, 8, and 4.9 does not have a right angle. The sides do not satisfy the Pythagorean Theorem, and therefore, the triangle is not a right angle triangle.

If you are verifying other triangles, remember that the Pythagorean Theorem is the key to determining whether a triangle is a right angle triangle.