 Hi and welcome to the session. Let's work out the following question the question says on a horizontal plane There is a vertical tar with a flagpole on the top of the tar At a point nine meters away from the foot of the tar the angle of elevation of the top and bottom of the flagpole are 60 degree and 30 degree respectively find the height of the tar and flagpole mounted on it So let's start with the solution to this question Let the height of flag be H meter and the height of the tar that is BCB capital H meter we see that in Triangle a BC 10 30 degree will be equal to BC divided by a B Now the value of 10 30 degree is 1 by root 3. So we have 1 divided by root 3 is equal to H divided by 9 because a B is equal to 9 This implies that H is equal to 9 divided by root 3 now We can multiply the numerator and denominator by root 3 on doing this we get H is equal to 9 root 3 divided by 3 and that is equal to 3 root 3 now the value of root 3 is 1.732 so this becomes equal to 5.196 meters Now let us consider triangle a BD. So in triangle a BD we have 10 60 degree is equal to BD divided by a B now again we put in the values here so this implies that root 3 is equal to small H plus capital H divided by 9 or root 3 is equal to H plus 3 root 3 because we've just found out that capital H is equal to 3 root 3. So we have this divided by 9 Now this implies 9 root 3 is equal to H plus 3 root 3 or H is equal to 9 root 3 minus 3 root 3 This is equal to 6 root 3 that is further equal to 6 multiplied by 1.732 and 6 into 1.732 10.3 9 2 meters So our answer to this question is that height of the tar that is capital H is equal to 5.196 meters and The flag mounted on it that is small H is equal to 10.392 meters So I hope that you understood the solution and enjoyed the session. Have a good day