Will the Pythagorean Theorem work with a non-right triangle?

Answer 1

no, it won't..

HOWEVER there are some other theorems through which you can calculate the length of a certain side of a triangle given the lengths of the other the sides.

Likewise it is also possible to calculate (through analytical geometry) the area of any triangle given the lengths of all sides.

So, practically, given the lengths of at least two sides of a triangle, you can calculate the length of the third side and then calculate the total area of the triangle.

(8th grade mathematics)

Answer 2

* Not usually. The ratios among the sides of right triangles are special and the right angle is what makes these ratios work. No right angle means no special relationship. The only exception is when you are using the altitude of a non-right triangle in a

Let's say there is an isosceles triangle with a base of X units in length. The altitude of any triangle is perpendicular to the base. This means that the altitude creates two right triangles. The altitude of an isosceles triangle is not only perpendicular, it also bisects the base, let's say Y. For this triangle, you have enough information to find the lengths of the congruent sides by using the Pythagorean Theorem.

Answer 3

i'm undecided what you propose by making use of proving the lengths are superb. you could instruct that the triangle is a incredible triangle (one nook is ninety levels) making use of the Pythagorean theorem. For a incredible triangle the sum of the sq. of the two short aspects is comparable to the sq. of the hypotenuse (the longest element). If A and B are the quick aspects (6 and 14) and C is the hypotenuse (15.23) then for this to be a incredible triangle A^2 + B^2 = C^2 considering the fact that 6^2 + 14^2 does equivalent 15.23^2 (approximately) this could be a incredible triangle.

Answer 4

It is stated in the theorem itself that it only works for right triangles, so obviously it doesn't work in oblique triangles, but :
for right triangles: a² + b² = c²
for acute triangles: a² + b² > c²
for obtuse triangles: a² + b² < c²

But the last 2 statements are not included in the pythagorean theorem(they are different theorems, which are not that famous so it doesn't have a distinctive name).

^_^

Answer 5

No it will not. The Pythagorean Theorem only applies to right triangles.

Answer 6

No.

However, the Law of Cosines is a generalization of the Pythagorean Theorem; c^2 = a^2 + b^2 -2ab cosγ
where γ is the angel opposite the side c.

This reduces to the Pythagorean theorem when γ is a right angle.

Answer 7

If p,b,h are sides of the triangle (p perpendicular, b base, h hypotenuse), and x is the base angle. Then b=hcosx and p = hsinx (since right angle triangle).
squaring and adding we get the Pythagoras theorem. This is true only for a right angled triangle.

Answer 8

The answer no is correct. But here's something that can come in handy...

If...
1. a^2 + b^2 = c^2; then you have a RIGHT triangle
2. a^2 + b^2 > c^2; then you have an ACUTE triangle
3. a^2 + b^2 < c^2; then you have an OBTUSE triangle

Answer 9

No. You have to use decoder triangles (30-60-90 or 45-45-90) or you can use Sin, Cos, and Tan.

Answer 10

NO! But you can use the law of cosines:
c^2 = a^2+b^2 - 2abcosC
(when triangle ABC is right, cos C = cos90 = 0)