My computer table has a square hole for a monitor. The diagonal of the hole (creating two 45-45-90 triangles)

Question

My computer table has a square hole for a monitor. The diagonal of the hole (creating two 45-45-90 triangles) is 24 inches. Will a monitor measuring 18 inches by12 inches fit? Please show work 

Answer 1

We can calculate the sides of the square hole in the desk by using the sine law, which is the sine of an angle = the length of the opposite side divided by the length of the hypotenuse.

 

in algebraic terms, sine ∠A = opposite/hypotenuse

so, sine ∠A x hypotenuse = opposite

 

the sine of 45^o is 0.7071, and the length of the hypotenuse is 24 inches

so, 0.7071 x 24 inches = the length of the opposite side = 17 inches

 

so, it appears that the monitor will not fit.