Question

One leg in a right triangle is 11 ​m, and the hypotenuse measures 11√2 m. Find the length of the other leg.

Answer 1

`\boxed{11m}`

Explanation:

Method #1: 45-45-90 Triangle

You can use the rules for a 45-45-90 triangle. These are:

→ Each 45-45-90 triangle is a right triangle with two additional 45° angles.

→ The triangle will have 2 legs, x, and one hypotenuse, x√2.

Therefore, because the problem gives values for one leg and the hypotenuse, the value for the one leg is equal to the value for the unsolved leg.

Method #2: Pythagorean Theorem

You can use the Pythagorean Theorem to solve for a missing side in a triangle. Please note, however, that the Pythagorean Theorem only works on right triangles.

The Pythagorean Theorem is defined as
`a^(2) + b^(2) = c^(2),` where a and b are both legs of the triangle and c is the hypotenuse.

Therefore, substitute the known value for a, 11, and the known value for c, 11√2. Then, evaluate each value to its power (except for b - it is unsolved) and simplify the equation with basic algebraic methods. Once your equation is down to
`b^(2)= ?`, you should take the square root of both sides of the equation to get the value for b.

`11^(2) +b^(2) =(11√(2) )^(2)\\121 + b^(2) = 242\\b^(2)=121\\b=11`