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A a right triangle has a hypotenuse length of 21 meters. It has
one leg with a length of 15 meters. What is the length of the other leg?
Express your answer as a square root.

1 Answer

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√216 meters

Step-by-step explanation:

» Concepts

The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs is equal to the length of the hypotenuse squared. It's represented as an equation of a² + b² = c², where a & b are the legs, and c is the hypotenuse

» Application

To find the length of the other leg, we have to plug in the values of b and c into the equation. B would be 15 meters, and c would 21 meters.

» Solution

Step 1: Simplify both sides of the equation.

- [tex]a^2+15^2+21^2[/tex]
- [tex]a^2+225=441[/tex]

Step 2: Subtract 225 from both sides.

- [tex]a^2+225-225=441-225[/tex]
- [tex]a^2=216[/tex]

Step 3: Take square root of both sides.

- [tex]\sqrt{a^2} = \sqrt{216}[/tex]
- [tex]a = \sqrt{216}[/tex]

Therefore, the length of the other leg is √216 meters.
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