A vertical pole of total height 15 m is divided into two parts. The lower part has a height of 5 m and the upper part has a height of 10 m. At a point on the ground, the upper part of the pole subtends an angle whose tangent is 1 2 . The possible distances of this point from the base of the pole are:

Step-by-step solution

Let the distance of the point from the base of the pole be x . Let the angle of elevation of the top of the pole be and the angle of elevation of the partition be . From the given data, the total height of the pole is 15 m and the height of the lower part is 5 m. Therefore, = 15 x and = 5 x . The angle subtended by the upper part at the point is = - . We are given that = 1 2 . Using the identity ( - ) = - 1 + , we get: 1 2 = 15 x - 5 x 1 + ( 15 x ) ( 5 x ) 1 2 = 10 x 1 + 75 x^2 1 2 = 10x x^2 + 75 x^2 + 75 = 20x x^2