We have Pythagoras' Theorem and SOHCAHTOA for right-angled triangles. These approaches, however, do not work for non-right-angled triangles. We have **the cosine rule**, the sine rule, and a new area formula for non-right-angled triangles. These methods can be used to find areas of any triangle with an angle greater than or equal to 120 degrees.

The Pythagorean theorem asserts that the area of the square whose side is the hypotenuse (the side opposite the right angle) in any right triangle is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). Because the area of a square is equal to the square of its length, this formula can be written as the product of the lengths of the two legs times the height. For example, the area of the right triangle with legs 7 and 8 is 49, which is equal to 49 * 28 = 1456.

The rule for right triangles is that the ratio of **the longest side** to the shortest side is the same as the ratio of the longest side of the resulting rectangle to the short side of that rectangle. In our example, the length of the right triangle's hypotenuse is 14. The length of the eighth side of the rectangle is 8, so the length of **its seventh side** is 8/7 of 14, or 1.142857.... Similarly, the length of the seventh side of the right triangle is 7/8 of 14, or 0.875000.... The ratios of the long sides of the right triangle and the resulting rectangle are therefore the same, which means that the ratio of the long side of the right triangle to the short side of that triangle is the same as the ratio of the long side of the resulting rectangle to its short side.

Pythagoras' theorem only applies to right-angled triangles, thus you can use it to determine whether or not a triangle has a right angle. If you find that a triangle does have a right angle, then it is safe to say that Pythagoras' theorem can be used with this triangle.

In general, all triangles whose angles add up to 180 degrees are called "right-angled". These include all equilateral triangles as well as those with some other shape of triangle. However, not every triangle that does not share two identical sides with another triangle is right-angled. For example, any triangle composed of **two lines** without **any points** in common is non-right-angled. There are also right-angled triangles that do not satisfy the precondition that their angles add up to 180 degrees, such as a triangle with an angle of 120 degrees. However, we can still use Pythagoras' theorem on these triangles because they are still right-angled triangles after a small modification: We reflect the triangle across one of the angles to obtain a new triangle that does satisfy the precondition. This process will always allow us to apply Pythagoras' theorem to **a right-angled triangle**.

In conclusion, yes, Pythagoras' theorem can be used with all triangles.

The Pythagorean Theorem and Right Triangles

- The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.
- The side opposite the right angle is called the hypotenuse (side c in the figure).

There are various methods for calculating the area of a triangle. For example, the area of a triangle equals half the base times the height, according to the fundamental formula. Of course, this formula only works if you know the height of the triangle. If you only know the length of one of the sides of the triangle, then you can use these formulas to calculate the remaining side.

In practice, you usually don't need to calculate the area of a triangle exactly. You only need to know whether the triangle is equilateral, isosceles, or scalene. These terms will help you determine which method should be used to estimate the area.

The area of a triangle is equal to 1/2 base x height. This formula works for **any type** of triangle, including those with arbitrary angles. However, it may not give you the exact answer. There are several methods used by mathematicians to solve **this problem** efficiently. One such method is to use the area formula and divide the result by 2 until the number of decimal places reaches some specified limit. For example, if the limit is set at **5 digits** after the decimal point, then the equation would look like this: 0.5 x 10^(-5) = 0.005. Since 0.005 is less than 0.01, we can conclude that this triangle has an area less than 1 square inch.