Grade 10Trigonometry

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

satyam

11 Years agoGrade 10

6 Answers

Harsh Patodia

11 Years ago

Hi Student

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

Ravi

11 Years ago

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,
$\sin^{2}\theta + \cos^{2}\theta =1$ ;
substitute the value in terms of P,B and H. to get to the pythagorus theorem.

Saurabh Kumar

11 Years ago

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

S. Agarwal

11 Years ago

Hi !
The solutions provided by Ravi and Harsha are infact corollaries.And saurabh used and Euclidian method!!!!
Sadly, there are no trigonometric proofs [of the Pythagorean theorem],because all of the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean theorem; because
of this theorem we say sin2 A + cos2 A = 1 etc.

For more information: Google “On the Possibility of Trigonometric Proofs of the Pythagorean Theorem”