Question

two persons are standing on the opposite sides of a tower they observe the angles of elevation of the top of the tower to 45 degree and 60 degree respectively find the distance between them if the height of the tower is 75 metre

Answer 1

Answer:

Let AB be the tower of height 70m.

Now,

For first person:-

θ=50°

AB=70m

As we know that,

tanθ=

Base

Perpendicular

Therefore,

In △ABD,

tan50°=

BD

AB

⇒BD=

tan50°

70

.....(1)

Similarly, for second person:-

θ=25°

AB=70m

In △ABC,

tan25°=

BC

AB

⇒BC=

tan25°

70

.....(2)

Therefore,

Distance between the two people

=BC−BD=

tan25°

70

−

tan50°

70

=70(

tan25°

1

−

tan50°

1

)

=70(

tan25°

1

−

2tan25°

1−tan

2

25°

)

=

tan25°

70

(1+tan

2

25°)

=(

tan25°

70

)sec

2

25°

=

sin25°cos25°

70

=

sin50°

140

Hence the distance between the two peope is

sin50°

140

.