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°
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Answer:
45 option ç may be is right
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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°
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