Solve Pythagoras theorem
Understand the Problem
The question is asking to solve or apply the Pythagorean theorem, which relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. We will use this theorem to find the length of a side if two sides are given or to solve related questions.
Answer
To find the missing side, use the Pythagorean theorem: $c = \sqrt{a^2 + b^2}$ or $a = \sqrt{c^2 - b^2}$.
Answer for screen readers
The length of the missing side is determined through the application of the Pythagorean theorem with appropriate values substituted.
Steps to Solve
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Identify the sides of the triangle First, determine which sides of the right triangle you have. Typically, you will have the lengths of two sides: the legs (let's call them $a$ and $b$) and the hypotenuse (let's call it $c$).
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Apply the Pythagorean theorem formula According to the Pythagorean theorem, the relationship between the sides is given by the equation: $$ c^2 = a^2 + b^2 $$ Identify which side is missing and rearrange the formula as necessary.
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Calculate the missing side If you need to find the hypotenuse ($c$), square the lengths of the legs ($a$ and $b$) and add them: $$ c = \sqrt{a^2 + b^2} $$
If you need to find one of the legs (say $a$), rearrange the formula: $$ a = \sqrt{c^2 - b^2} $$
- Perform the calculations After rearranging the equation, plug in the known values and perform the calculations to find the length of the missing side.
The length of the missing side is determined through the application of the Pythagorean theorem with appropriate values substituted.
More Information
The Pythagorean theorem is foundational in geometry and is widely used in various fields such as physics, engineering, and computer science. It allows for calculating distances, angles, and heights in right-angled scenarios.
Tips
- Forgetting to square the sides properly, which can lead to incorrect results.
- Mixing up the sides by labeling the hypotenuse as one of the legs. Always remember that the hypotenuse is the longest side opposite the right angle.
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