prove pythagoras theorem using trigonometry..........................plz explain briefly

Hi Student

We know using trigonometry
sin = p/h
and cos = b/h
and using identity sin² + cos² =1
p²/h² +b²/h² =1
p² + b² = h² (Hence proved)

For a right angled triangle, with sides P(perpendicular), B(base) and H(hypotenuse);
write the trig. ratios in terms of P, B and H with any of the internal angle of the triangle.

Using the identity,
;
substitute the value in terms of P,B and H. to get to the pythagorus theorem.

Pythagorean Theorem, The theorem states that:

"The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs”.


This theorem is talking about the area of the squares that are built on each side of the right triangle.


Accordingly, we obtain the following areas for the squares, where the green and blue squares are on the legs of the right triangle and the red square is on the hypotenuse.



area of the green square is
area of the blue square is
area of the red square is



From our theorem, we have the following relationship:

area of green square + area of blue square = area of red square or