Question

if two towers of height h1 andh2 subtend angles of 60 and 30 respectively at the mid point of the line joining their feet , then h1: h2 is? (a) 3:1 (b) root 3 : 1 (c) 1: root 3 (d) 1 :3

Answer 1

Hi,

Draw the rough diagram with the data

given

A
I
|
|
| h1 lD
I l
l lh2
B________P_______C
x x
Join A to P and D to C

Height of the one tower = AB = h1

Height of the second tower = CD = h2

Two towers subtend angles of 60 and 30

degrees at P , and P is the mid point of BC

Let BP = PC = x

i ) In triangle APB , angle B = 90

tan < APB = AB / BP

tan 60 = h1 / x

( sqrt 3 ) = h1 / x ------( 1 )

ii ) In triangle DCP ,

Angle C = 90,

tan
tan 30 = h2 / x

1 / ( sqrt 3 ) = h2 / x -------( 2 )

Find the ratio of ( 1 ) and ( 2 )

Therefore,

(Sqrt 3 ) / [ 1/ sqrt 3 ] = (h1 /x ) / ( h2 / x )

(Sqrt 3 )(sqrt 3 ) / 1 = h1 / h2

3 /1 = h1 / h2

Therefore,

h1 : h2 = 3:1

Option ( a ) is correct .

I hope this helps you.

:)

Answer 2

this is the correct answer this will definitely help you guys. .