Question

in a right angle triangle the product of two sides is equal to the half of the square of the third side i.e. hypotenuse one of the acute angles may be:
a)60°
b)30°
c)45°
d)15°​

Answer 1

Answer:

45 option ç may be is right

Answer 2

Answer:

C) 45°

Step-by-step explanation:

we have, z²/2 = xy     ------- 1

z² = x² + y²       ( by P.G.T. )  ------- 2

substituting the value of z² from eq. 1 in eq. 2, then we get

⇒ (x² + y²)/2 = xy

⇒ x² + y² = 2xy

⇒ x² + y² - 2xy = 0

⇒ ( x-y )² = 0

⇒ x-y = √0

⇒ x-y = 0

⇒ x  = y

∵ angle opp. to equal side of a triangle are equal

∴ in ΔABC, ∠P = ∠P

Now in ΔABC,

⇒ ∠ABC + ∠BAC + ∠ACB = 180°

⇒ 90° + P + P = 180

⇒ 2P = 90°

⇒P = 90°/2

⇒ P = 45°