Question

two points A and B are on the same side of a tower and in the same straight line with its base the angle of depression in of these points from the top of the tower and 60 degree and 45 respectively if the height of the tower is 15 M then find the distance between the points

Answer 1

Th answer is 5√3(√3-1)m

The method is provided in the picture:

Answer 2

Let AB is tower and two points C and D are present same side of tower as shown in figure.
Let the distance between C and D is d .
And the distance between tower and point C is x

Now, ∆ABC ,
Here ∠ACB = 60°
So, apply tan∠ACB = tan60° = AB/BC
AB is given e.g., AB = 15m
∴ tan60° = √3 = 15/BC
⇒BC = 15/√3 = 5√3 m

Now, for ∆ABD
∠ADB = 45°
Apply tan∠ADB = tan45° = AB/BD
⇒ 1 = 15/(BC + CD)
⇒BC + CD = 15m
Put BC = 5√3m
∴ CD = 15m - BC = 15m - 5√3m

Hence, distance between C and D = 5√3(√3 - 1)m