Question

Use the Pythagorean Theorem to find the length of the third side of the right triangle. Leave any irrational answers in radical form. Given sides: 24, 7, c.

a) c= 625
​b) c= 481
​c) c= 625+481
​d) c=31

Answer 1

To calculate the length of the third side 'c' in a right triangle given sides 24 and 7, square each side and add the results, then take the square root: (√(24² + 7²)) = 25.

Step-by-step explanation:

To find the length of the third side 'c' of a right triangle when given the other two sides using the Pythagorean Theorem, we use the equation a² + b² = c², where 'c' is typically the hypotenuse. In this case, we have two sides given as 24 and 7. According to the theorem, we calculate the length of 'c' as follows:

1. First, square both of the given sides: 24² = 576 and 7² = 49.
2. Add these squares together: 576 + 49 = 625.
3. Since c² = 625, we find 'c' by taking the square root of 625: c = √625.
4. Finally, the length of side 'c' is √625, which simplifies to 25 when considering the principal square root.

Therefore, the length of the third side 'c' of the right triangle is 25 units.