What is the length of the hypotenuse of the right angle ABC if AB = 5 and AC = 6
Pythagorean Theorem
5^2 + 6^2 = Hypotenuse squared
H^2 = 5^2 + 6^2
= 61
H = √61
To find the length of the hypotenuse of a right-angled triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we are given the lengths of the two sides adjacent to the right angle, AB = 5 and AC = 6. Let's label the hypotenuse BC.
The Pythagorean theorem equation for this triangle is:
BC^2 = AB^2 + AC^2
Substituting the given values into the equation:
BC^2 = 5^2 + 6^2
BC^2 = 25 + 36
BC^2 = 61
To find the length of BC, we take the square root of both sides of the equation:
BC = sqrt(61)
Therefore, the length of the hypotenuse BC is approximately equal to the square root of 61.