# Problem Solving Pythagorean Theorem In order to calculate the hypotenuse, we apply the Pythagorean theorem.Therefore each side of the rhombus (each hypotenuse) measures 10. Since these are all the same, we only need to multiply by 4: Perimeter = 4·10 = 40 We have to take into account that that the units of measurement are not equal.

In order to calculate the hypotenuse, we apply the Pythagorean theorem.

A few of them are: Also Pythagorean Triples can be created with the a Pythagorean triple by multiplying the lengths by any integer. We see looks like the legs of a right triangle with a multiplication factor of 111.

For example, Right triangle has legs of length and .

the 3 numbers can be the lengths of the sides of a right triangle.

Among these, the Primitive Pythagorean Triples, those in which the three numbers have no common divisor, are most interesting.

The situation is the following: The line Sun-Moon and the line Earth-Moon form a 90 degree angle, if not, we would not see The Moon in its first quarter. Therefore we know the distance Earth-Moon (a) and the distance Earth-Sun (h).

So, we can calculate the distance Sun-Moon (b) applying the Pythagoras' Theorem: We do not calculate the value of b, because the distance from Earth-Sun is a lot bigger than the distance Earth-Moon and, by approximation, we obtain a similar value to the distance Earth-Sun.So, the height will be, approximately Exercise 7 The distance Sun-Earth-Moon: Let us suppose that The Moon is in the first quarter phase, which means that from Earth we see it the following way: The white side of The Moon is the side we see (the side illuminated by The Sun).We know that the distance from Earth to The Moon is 384100Km, and the Earth to The Sun is around 150 million Kilometers.We can write them all in meters, so 70 cm = 7 dm = 0.7 m The triangle we have is The height is one of the sides.We apply the Pythagorean theorem to calculate it: Hence But a has to be positive, because it is a unit of measurement.We wish to calculate the distance between The Moon and The Sun in this phase (considering the distances from the centers).Lay out the exercise, but it is not necessary to calculate a result.As we will see in the exercises of this section, there are numerous applications of the theorem in real life.In addition, the theorem has uses in advanced mathematics as well (vectorial analysis, functional analysis…). The Pythagorean theorem is one of the most known results in mathematics and also one of the oldest known.For instance, the pyramid of Kefrén (XXVI century b.