Question

if in a right angled triangle the square of the hypotenuse is equal to twice the product of the other two sides then one of the acute angles of the triangle is ?

Answer 1

Let the sides be a,b and c
Then a^2=b^2+c^2
2bc=a^2(given)
2bc=b^2+c^2
b^2+c^2-2bc=0
(b-c)^2=0
b-c=0

Answer 2

Answer:

45°

Step-by-step explanation:

Let hypotenuse be 'h', adjacent : 'x' , opposite: 'y' of the triangle.

By Pythagoras theorem : h^2 = x² +y²    -eq1

Given,

         h² = 2xy                                             -eq2

Using eq1 & eq2

2xy=  x² +y²

x² +y² -2xy=0

This is possible only when x=y, if adjacent is same as opposite, the angle has to be 45°

As tan(45°)= 1 = opposite/adjacent

Therefore, opposite = adjacent & answer = 45°