Question

Does the triangle whose diameter are 21, 72, and 75 have a right angle in it?

Answer 1

√(21² + 72²) = √(441 + 5,184) = √5,625 = 75

So this is a right triangle.

Answer 2

A triangle with sides 21, 72, and 75 forms a right-angled triangle, as it satisfies the Pythagorean theorem equation, confirming the presence of a right angle.

Step-by-step explanation:

The question pertains to whether a triangle with sides measuring 21, 72, and 75 units forms a right-angled triangle. According to the Pythagorean theorem, in a right-angled 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. To verify this, we need to check if the equation a2 + b2 = c2 holds true for the given side lengths.

For the triangle with sides 21, 72, and 75, let's see if the following equation is satisfied:

212 + 722 = 752

441 + 5184 = 5625

5625 = 5625

The equation does hold true, which indicates that the triangle with sides measuring 21, 72, and 75 does indeed have a right angle.