In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e., hypotenuse. One of the acute angle must be

A. 60°

B. 30°

C. 45°

D. 15°

Answer: Option C

Solution(By Examveda Team)

According to question,
Given :

ab = $$\frac{{{C^2}}}{2}$$ . . . . . . . . . . (i)
∴ In ΔABC
Using Pythagoras theorem
AC² = AB² + BC²
c² = a² + b² . . . . . . . . . . . (ii)
Put the value of C² in equation (i)
2ab = a² + b²
a² + b² - 2ab = 0
(a - b)² = 0
∴ a - b = 0
a = b
If a = b means ABC is isosceles right angle triangle it means
∠A = 45°     ∠B = 45°