Question

AB is a vertical pole whose end A is on the level ground.C is the midpoint of AB.P is the point on the levelground.The portion CB substends an angle of beta at P.If AP=nAB.Find tanbeta.

Answer 1

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=X/2

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 (Alpha) = (X/2) / nX = 1/2n

tan (Alpha +Beta) = X/nX = 1/n

We know the formula: tan (x+y) = [tan x + tan y]/ [1- tan x * tan y]

Therefore, 1/n= [tan Beta + 1/2n ] / [ 1- (tan beta*1/2n)]

After solving the above equation,

tan Beta = n/(2n^2+1)

Answer 2

Answer:

n/2n^2+1

Step-by-step explanation:

Answer is in above pic.