Question

a boy 1.6m tall is 20m away from a tower and observes that the angle of elevation of the top of the tower is 60 degree. Find the height of the tower.

Answer 1

let AC be tower 
DE=1.6m as BC =1.6 m 
DC =20 m as BE = 20 m
so, in triangle ABE
tan 60= AB/BE
√3 =AB/20
AB =20√3m
so,the height of the tower = AC =AB+BC =20√3+1.6
                                                               =20×1.732+1.6 =34.64 +1.6
                                                                =36.24 m

Answer 2

see the link for the figure of the question

let AB be the height of tower and CD be the boy

we have CD = 20m and CD = 1.6m

also BD = CE = 20m

in triangle ACE ,

tan60 = P/B = AE/20

√3 = AE/20

so, AE = 20√3m

also CD =  BE = 1.6m

Height of tower = AE+BE

=(20√3+1.6)m