Question

draw a diagram for the following situation; two men an either side of a top at the angles of evelvation 30 and 60 respectiviely.

Answer 1

Let AB be the height of the temple and P and Q are the two men on either side of the temple.

Given that,

AB=30 m, ∠APB=30

∘

,∠AQB=60

∘

In △ABP,

tan(∠APB)=

PB

AB

tan30

∘

=

PB

30 m

PB=30

3

m

In △ABP,

tan(∠AQB)=

QB

AB

tan60

∘

=

QB

30 m

QB=

3

m

30

QB=10

3

m

Now, PQ=PB+QB=30

3

m+10

3

m

So, PQ=40

3

m

Therefore, distance between two men, i.e. PQ=40

3