Find the height of a given tower using mathematical modelling.

From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 30^@ . The angle of elevation to the top of a water tank (On the top of the tower) is 45^@ . Find the height of the tower and the depth of the tank.

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^@ . From a point 20maway from this point on the same bank, the angle of elevation of the top of the tower is 30^@ (see fig.). Find the height of the tower and the width of the canal.

From the top of a building 15 m high, the angle of elevation of the top of a tower is found to be 30^@ . From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the distance between the tower and the building.

On a horizontal plane there is a vertical tower with a flag on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60^@ and 30^@ respectively. Find the height of the tower and flag pole mounted on it.

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^@ . At a point Y, 40 m vertically above X, the angle of elevation is 45^@ . Find the height of the tower PQ and the distance XQ.

The radius and the height of a right circular cone are in the ratio 5 : 12. If its volume is 314 cm^3 , find the slant height and the radius of the cone. [Use pi = 3.14]

We have given the timings of the gold medalists in the 400-metre race from the time the event was included in the Olympics, in table below. Contruct a mathematical model relating years and timings. Use it to estimate the timing in the next Olympics.

Find and correct the errors in the following mathematical statements. (a+5)/5 =a+1 .

The length of a shadow of a tower 24 metres high is 20 metres.Under the same conditions,find the height of a same conditions,find the height of a tree,the length of whose shadow is 15 m.