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bulgar [2K]
3 years ago
12

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

Mathematics
1 answer:
ipn [44]3 years ago
4 0

Answer:

\boxed{11m}

Step-by-step 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, <em>x</em>, and one hypotenuse, <em>x</em>√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 <u>right</u> triangles.

The Pythagorean Theorem is defined as a^{2} + b^{2} = c^{2}, where <em>a</em> and <em>b</em> are both legs of the triangle and <em>c</em> is the hypotenuse.

Therefore, substitute the known value for <em>a</em>, 11, and the known value for <em>c</em>, 11√2. Then, evaluate each value to its power (except for <em>b </em>- 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 <em>b</em>.

11^{2} +b^{2} =(11\sqrt{2} )^{2}\\121 + b^{2} = 242\\b^{2}=121\\b=11

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