Question

In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides, find the acute angles of the triangle

Answer 1

Answer:

Step-by-step explanation:

45 and 45 degrees

Answer 2

let ΔABC be the given triangle right angled at B

AC is the hypotenuse

Given:

AC²=2*AB*BC —(1)

We know that AC²=AB²+BC²

Substituting this value in (1)

2*AB*BC=AB²+BC²

AB²+BC²-2*AB*BC=0

This is of the form (a-b)²

Therefore, (AB-BC)²=0

AB-BC=0

AB=BC

ΔABC is an isosceles triangle

Therefore the acute angles are 45° each