How to find hypotenuse with adjacent and opposite?
Understand the Problem
The question is asking how to calculate the hypotenuse of a right triangle when given the lengths of the adjacent and opposite sides. This can be approached using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Answer
The hypotenuse $c$ is given by $c = \sqrt{a^2 + b^2}$.
Answer for screen readers
The length of the hypotenuse $c$ is given by the formula $c = \sqrt{a^2 + b^2}$.
Steps to Solve
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Identify the lengths of the sides First, let's denote the lengths of the adjacent side as $a$ and the opposite side as $b$.
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Apply the Pythagorean theorem The Pythagorean theorem states that the square of the hypotenuse $c$ is equal to the sum of the squares of the opposite and adjacent sides: $$ c^2 = a^2 + b^2 $$
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Solve for the hypotenuse To find the length of the hypotenuse $c$, take the square root of both sides: $$ c = \sqrt{a^2 + b^2} $$
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Calculate using specific values If you have specific values for $a$ and $b$, substitute them into the equation and perform the calculation: $$ c = \sqrt{(length_of_a)^2 + (length_of_b)^2} $$
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Final result After performing the substitution and the math, you will have the length of the hypotenuse.
The length of the hypotenuse $c$ is given by the formula $c = \sqrt{a^2 + b^2}$.
More Information
The Pythagorean theorem is a fundamental principle in geometry, especially in right triangles. It's widely used in various fields such as architecture, construction, and physics.
Tips
- Forgetting to square the lengths of the sides before adding them. Always remember to calculate $a^2$ and $b^2$ before summing.
- Taking the square root of both sides incorrectly. Ensure to apply the square root only after summing the squares of the sides.
