Two poles of equal height stand vertically opposite to each other on either side of the road, which is 100 m wide. From a point on the road between the poles, the angle of elevation of the tops of the poles are 30 degree and 60 degree . Find the heights of the poles. Also find the distance of the point from the feets to the poles.
Answers
Answer:
Bottom distance = 100 m.
Angle of Elevation
Angle of Elevation
Height of the two poles.
Distance of the points from the feet of the poles.
Let the height of both the poles will be h m.
Let the distance from point A and B be x m.
Hence according to the Question , the distance from point B will be (100 - x) m.
To find the height of pole (in terms of h) with respect to angle 60°.
Using tan θ and substituting the values in it, we get :
Hence the distance between base of A and B (in terms of h) is √3/h
Now , by using the tan θ and substituting the values in it, we get :
Now , by substituting the value of x from equation (i) , we get :
Hence the Height of two towers is 25√3 m.
Since, we have taken the base distance as x and we know the value of x in terms of h i.e,
Now, putting the value of h in the above equation , we get :
Hence, the base distance from A to B is 25.
Distance between B and C :
We know that the distance between B and C is (100 - x) m.
So by putting the value of x in it , we get :
Hence the distance between B and C is 75 m.