 Hello and how are you all today? The question says two pillars of equal height stand on either side of a roadway which is 150 meter wide. From a point on the roadway between the pillars the elevation of the top of the pillars are 60 degree and 30 degree. Find the height of the pillars and the position of the point. So here let us have a diagram to model the situation. Let this be the diagram where A and B are the two equal pillars who are standing on the either sides of the roadway which is 150 meter wide. Now from a point B the angle of elevation is 60 and 30 respectively. We need to find out the height of these pillars and position of this point. So here let this distance md be equal to x therefore the distance of Bm will be 150 minus x, right? And let the height of the pillar that is pillar be equal to h meters. Distance of the point from the first let it be cd be x meters, right? Now we will be finding out edge in respect of this triangle and this triangle. Let us divide our page into two columns. Now here in triangle AB or A and B 30 degree is equal to AB upon Bm, right? This implies 1 by root 3 that is the value of tan 30 is equal to h that is AB upon 150 minus x. This further implies h is equal to 150 minus x upon root 3. This be the first equation. In the same manner in triangle tan 60 degrees equal to cd upon md that implies root 3 is equal to h upon x that further implies root 3 x is equal to h. Let this be the second equation. Now we know that therefore we have 15x upon root 3 equal to root 3. On simplifying we have 150 minus x is equal to 3x that is 150 equal to 4x that is x is equal to 150 upon 4. That implies that the value of x is coming out to be 37.5 and with the help of this value of x we can find out edge by substituting x in any of these two equations. So on substituting the value of h we get h is equal to root 3 into x that is 37.5 that implies h is equal to 1.73 into 37.5 meter that is further equal to 64.95 meter. Right we can also take the value of root 3 to 3 decimal places that is 1.732 to get the required answer. Now the answer is thus the height of the pillar 64.95 meter position of the point pillar that we took as cd is 37.5 meter away. In the session hope you understood.