The top and bottom of a tower were seen
to be at angles of depression 30° and 60° from the top of a
hill of height 100 m. Find the height of the tower  Select
A) 64.67 m
B) 66.67 m
C) 68.67 m
D) 56.67 m
E) 46.67 m

Rationale: by making a diagram ac represents the hill and de represents the pole given that ac = 100 m anglexad = angleadb = 30 ° ( ∵ ax | | bd ) anglexae = angleaec = 60 ° ( ∵ ax | | ce ) let de = h then , bc = de = h , ab = ( 100 - h ) ( ∵ ac = 100 and bc = h ) , bd = ce tan 60 ° = acce = > 3 √ = 100 ce = > ce = 1003 √ - - - ( 1 ) tan 30 ° = abbd = > 13 √ = 100 − hbd = > 13 √ = 100 − h ( 1003 √ ) ( ∵ bd = ce and substituted the value of ce from equation 1 ) = > ( 100 − h ) = 13 √ × 1003 √ = 1003 = 33.33 = > h = 100 − 33.33 = 66.67 m i . e . , the height of the pole = 66.67 m answer : b
Answer: B