What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 9 and 1?

Question

James Adkins · Accepted Answer

≈ 9.06

Using #color(blue)" Pythagoras' Theorem "# which states " the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides' If hypotenuse = h and the other 2 sides are a and b then # h^2 = a^2 + b^2# here let a = 9 and b = 1 , then # h^2 = 9^2 + 1^2 = 81 + 1 = 82 # now #h^2 = 82 rArr h = sqrt82 ≈ 9.06#

Caroline Adams · Answer

undefined To find the length of the hypotenuse of a right triangle when the lengths of the other two sides are given, we use the Pythagorean theorem.

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.

So, if the lengths of the two other sides are 9 and 1, we have:

$a^2 + b^2 = c^2$

Substitute the given values:

$9^2 + 1^2 = c^2$

Solve for $c^2$:

$81 + 1 = c^2$

$82 = c^2$

Take the square root of both sides to find the length of the hypotenuse:

$c = \sqrt{82}$

Therefore, the length of the hypotenuse of the right triangle is $ \sqrt{82} $ units.