Question

The adjoining figure shows two concentric squares of side length 3 and 4. The inner square is rotated about the centre by an angle theta, 0

Answer 1

Answer:

25.53°

Step-by-step explanation:

Side of inner square = 3

Side of outer square = 4

Let say after rotating inner square it touches side of outer square

dividing side in a & 4-a

a² + (4-a)²  = 3²

=> a² + 16 + a² - 8a = 9

=> 2a² -8a +7 = 0

a = (8 ± √64 - 56)/4

= (8 ± √8)/4

= 2 ±  1/√2

Tan θ = (2 - 1/√2)/(2 + 1/√2)

=> Tan θ =  (4 + 1/2 - 2√2)/(4 - 1/2)

=> tanθ = (9 - 4√2)/(7)

=> Tanθ = 0.4776

=> θ = 25.53°