Problem Solving Pythagorean Theorem

So, Now we isolate a, we can join both expressions obtaining a lineal equation: Knowing the value of x we can obtain y: Now we know how much each base measures and we can obtain the height.

The first equation was And we know that x = 1, so we have that The height a cannot be negative.

The Pythagorean Theorem is one of the most frequently used theorems in geometry, and is one of the many tools in a good geometer's arsenal.

A very large number of geometry problems can be solved by building right triangles and applying the Pythagorean Theorem. There are no more cases as the hypotenuse has to be greater than the leg.

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 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.

We know that By Pythagoras' Theorem, We replace the known values in the equations (a and b), obtaining: Remember that a square root squared is the radicand (what is inside the square root sign), so It follows that the hypotenuse measures approximately 2.24.

We do not indicate a unit of measurement because the activity did not provide one.


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