 Welcome to the session. I am Shashi and I am going to help you with the following question. Question says, a TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60 degrees. From another point 20 meters away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top 30 degrees height of the tower and the width of the canal. Let us now start with the solution. Where we can see in the figure, A B is the tower. It stands on a bank of a canal. Now C is a point on other bank of a canal such that angle of elevation of the top of the tower from this point is 60 degrees. Now on moving 20 meters away from this point that is on reaching point T, angle of elevation of top of the tower changes to 30 degrees. Now we are required to find out height of the tower and width of the canal. That is we have to find out A B and C B in the given question. Now we can simplify the given figure by drawing this simple diagram. Let us assume that height of A B is h meters and we see that this width of the canal is equal to x meters. So we can write let A B is equal to h meters is equal to x meters. We also know that angle A C B is equal to 60 degrees, elevation of top of the tower. We also know that angle A B B is equal to 30 degrees, elevation of top of the tower. First of all let us consider triangle A B C in right triangle A B C tan 60 degrees is equal to h upon x. Or we can say tan 60 degrees is equal to A B upon C B. So we can write in right triangle A B C tan 60 degrees is equal to A B upon C B. We know A B is equal to h meters and C B is equal to x meters. So we can write tan 60 degrees is equal to h upon x. Now we know tan 60 degrees is equal to root 3. So we can write root 3 is equal to h upon x. Same this expression as 1. Now we will consider triangle A B D in right triangle A B D is equal to A B. We know tan theta is equal to perpendicular upon base in this triangle. A B is perpendicular, B D is base and theta is at point D value of theta is equal to 30 degrees. Now we know A B is equal to h meters and B D is equal to x plus 20 meters. So we can write tan 30 degrees is equal to h upon x plus 20. Now we know tan 30 degrees is equal to 1 upon root 3. Now substituting 1 upon root 3 for tan 30 degrees. In this expression we get 1 upon root 3 is equal to h upon x plus 20. Now multiplying both the sides by x plus 20 we get x plus 20 upon root 3 is equal to h. We can simply write it as h is equal to x plus 20 upon root 3. Let us name this expression as 2. Substituting this value of h in expression 1 we get root 3 is equal to x plus 20 upon root 3. Upon x sides by x we get root 3x is equal to x plus 20 upon root 3. Multiplying both the sides by root 3 we get 3x is equal to x plus 20. Now subtracting x from both the sides we get 2x is equal to 20. Dividing both the sides by 2 we get x is equal to 10. Now we know x is equal to width of the canal that is vc. So we get is equal to x is equal to 10 meters. Now from expression 1 we know root 3 is equal to h upon x. Now substituting x is equal to 10 in this expression we get root 3 is equal to h upon 10. Other sides of this expression by 10 we get 10 root 3 is equal to h or we can write h is equal to 10 root 3 meters. Now we know h is the height of the tower so we get av is equal to h is equal to 10 root 3 meters. So height of the tower is equal to 10 root 3 meters and width of the canal is equal to 10 meters. So the required answer is 10 root 3 meters, 10 meters. This completes the session. Hope you understood the solution. Take care and have a nice day.