From the top of a pole house A in a street, the angles of elevation and…

Given:
Height of pole house A = 21 m
Angle of depression from top of A to foot of B = 30°
Angle of elevation from top of A to top of B = 60°
Let the distance between the houses be x m.
From the angle of depression:
tan 30° = 21/x
1/√3 = 21/x
x = 21√3
Now, let the height of house B be h m.
Difference in heights:
= h − 21
Using angle of elevation:
tan 60° = (h − 21)/(21√3)
√3 = (h − 21)/(21√3)
Cross multiply:
h − 21 = 21 × 3
h − 21 = 63
h = 84 m
Since the obtained answer does not match the options, let us verify carefully.
Using:
Distance = 21√3 ≈ 36.37
Now,
tan 60° = (h − 21)/36.37
√3 = (h − 21)/36.37
h − 21 = 36.37 × 1.732
≈ 63
h ≈ 84 m
The options provided do not contain the correct value.