TI-(x 15 45)

[Speed2001]

 

[Lokman Gökçe]

The problem has two solutions, x = 30 and x = 72, 083 ... (approximately). Since  x = 72, 083 ... is not rational number, we can't solve the problem geometrically.

But we can find these solutions with calculus. In that way in the triangles ABD and CDB we apply sine theorem, we yield that:

sin(60 + x).sinx = sin45.sin(x + 15). Although x < 75. Now we define the function f(x) = sin(60 + x).sinx - sin45.sin(x + 15). If we draw graph y=f(x), we see that this graph intersect with x-axis, at two points.