Angle of depression from the top of a lighthouse of two

Angle of depression from the top of a lighthouse of two boats are 45° and 30° due east which are 60 m apart. The height of the light house is :

As per given figure , we have
Let, the boats be at P, Q. So that PQ = 60m. Let, MA be the lighthouse.
Let, h = MA.

Then,	h	=	tan45°	= 1.	∴ h = MP
	MP

Again,	h	=	tan30°	=	1
	MP + 60				√3

∴ MP + 60

√3h or, h + 60 = √3h

∴ ( √3 - 1 )h = 60

∴	h =	60	h =	60 ( √3 + 1 )	30 ( √3 + 1 ) m
		√3 - 1		2