Two poles of equal heights are standing opposite to each other on either side of a road, which is 100 meters wide .from a point between them on the road, the angles of elevation of their tops are 30? and 60? .find the position of the point and also, the height of the poles. ( use = 1.73)

Distance to the pole from the vertex of the 60o angle = 25 mDistance to the second pole from the vertex of the 30o angle = 75 mHeight of the pole = 43.3

Step-by-step explanation:

The point is somewhere on the road. From that point, two poles can be seen at different angles of elevation. One is 30 degrees, and another is 60 degrees.

Call the height of the poles y and the point on the road as x meters away from the base of 60 degree angle to the base pole

Tan(60) = y/xTan(30) = y/(100 - x)  Isolate y for both equations
x*tan(60) = y(100 -x) * tan(30) = y  Since both boles are equal in height, equate the two equations.

(100 - x) * tan(30) = x*tan(60)

Using exact values (from the unit circle) tan(30) = sqrt(3)/3tan(60) = sqrt(3)(100 - x) * sqrt(3)/3 = x*sqrt(3)     Divide both sides by sqrt(3)(100 - x)/3 = x                              Multiply both sides by 3 100 - x = 3x                                  Add x to both sides100 = 4x                                       Divide by 4x = 25

The distance to the other pole = 100 - 25 = 75

y = x * sqrt(3)y = 25 * 1.73y = 43.3