How To Find The Missing Side Length In A Right Triangle Using The Pythagorean Theorem

Legs of a right triangle Chapter 5 (p. 254)

The sides adjacent to the right angle of a right triangle

A right triangle is a triangle in which one angle measures 90 degrees. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs.

If two legs of a right triangle are given, we can find the length of the third leg using the Pythagorean theorem which states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Mathematically,

a^2 + b^2 = c^2

where ‘a’ and ‘b’ are the lengths of the legs and ‘c’ is the length of the hypotenuse.

To find the length of the missing leg (let’s say it’s ‘a’), we can rearrange the formula as follows:

a^2 = c^2 – b^2

Then, we take the square root of both sides to find ‘a’:

a = sqrt(c^2 – b^2)

Alternatively, if we know the length of one leg (let’s say it’s ‘b’) and the hypotenuse (‘c’), we can use the same formula to find the length of the other leg (‘a’):

a^2 = c^2 – b^2
a = sqrt(c^2 – b^2)

In summary, if we have two sides (legs or hypotenuse) of a right triangle, we can use the Pythagorean theorem to find the length of the missing side.

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