Question

AB is a vertical pole with its foot B on a level of ground. A point Con AB divides such that AC : CB = 3:2. If the parts AC and CB subtend equal angles at a point on the ground which is at a distance of 20m from the foot of the pole, find the height of the pole.​

Answer 1

Step-by-step explanation:

Given:

AB is vertical pole with A at ground. C is midpoint of AB

P is another point in ground and Distance of AP= nAB

Let AB=X

So, AC=

2

X

AP=nX

Given that Beta is the angle subtended by BC at P

Assume Alpha is the angle subtended by AC, such that AB subtends an angle of (Alpha +Beta) at P

Therefore, tan (α)=

nX

(X/2)

=

2n

1

tan(α+β)=

nX

X

=

n

1

We know the formula: tan(x+y) =

[1−tanx∗tany]

[tanx+tany]

Therefore,

n

1

=

[1−(tanβ∗1/2n)]

[tanβ+1/2n]

After solving the above equation,

tanβ=

(2n

2

+1)

n