Pythagorean theorem: solving word problems
The Pythagorean Theorem helps with many everyday calculations. In math class, word problems simulate such situations. The article describes how you can go about solving such tasks.
The Pythagorean theorem - the basics
- In a right triangle, the hypotenuse is always the longest side of the triangle. Opposite her is the right one angle. The other two sides are called cathets.
- The Pythagorean theorem says that the square of the hypotenuse length is equal to the sum of the squares of the two cathetus lengths. As a formula, the Pythagorean theorem is written as follows: c2= a2+ b2. Here c is the hypotenuse and a and b are the two legs.
- The sentence group of Pythagoras also includes two sentences of Euclid, which also refer to calculations in right triangles, namely the cathetus sentence and the height theorem. This is where the two hypotenuse sections come into play, which are created by the construction of the height on the hypotenuse. The height is always perpendicular to the respective side of the triangle and begins at the opposite corner point. The height of the hypotenuse therefore always begins at the vertex of the right angle.
- According to the cathetus theorem, the square of a cathetus length corresponds to the product of the length of the hypotenuse and the length of the hypotenuse section adjacent to the cathetus.
- The theorem of heights says that the square of the height is equal to the product of the two hypotenuse sections.
Euclid's theorem of heights - a brief introduction with examples
Euclid's theorem of heights is often used as a mathematical "appendage" to the theorem of ...
How to solve the word problems
- Word problems often describe everyday problems. First check whether at least one right-angled triangle plays a role or whether it can be constructed from the known sizes. Only then can you possibly solve the problem with the Pythagorean Theorem. For example, the diagonals of rectangles can be calculated in this way.
- Make a sketch. This is especially helpful for more complex word problems.
- Enter all triangle sizes given in the sketch. With the Pythagorean Theorem you can solve the problem if at least two sides of the right triangle are given or can be derived from given quantities.
- In your sketch, mark the side of the triangle you are looking for with an x.
- Determine the hypotenuse and cathetus. Write down the Pythagorean theorem, inserting the known side lengths and the unknown side x into the formula.
- Rearrange the equation for x and calculate x.
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