Draw a figure based on given instructions:
Where SP = Statue
PB = Pedestal
Angles of elevation of S and P are 60° and 45° respectively.
Let AB = x, PB = h
(units are in meters)
From figure:
Right △ABS:
tan 60° = SB/AB
√3 = SB/AB
√3 = (h + 1.46)/x …(1)
Again, from right △PAB:
tan 45° = PB/AB
1 = PB/AB = h/x
h = x …(2)
Equation (1) implies
√3 = (h + 1.46)/h (using equation (2))
h = 1.46/(√3 – 1)
= 1.46/(√3 – 1) x (√3 + 1)/(√3 + 1)
= 1.46/2 x (√3 + 1)
= 2
Height of the pedestal is 2 meters.