The angle of elevation of the top P of a tower from the feet of one person standing due south of the tower is 45 ° and from the feet of another person standing due west of the tower is 30 ° . If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to

Step-by-step solution

Given that the elevation to the top of the tower from the feet of one person due south is = 45 ° Similarly the angle of elevation to the top of tower from the feet of another person to the west of tower is = 30 ° The given information can be represented in the form of a diagram as below: We need to find the distance A B . Let the distance of A , B from the tower be x 1 , x 2 . ⇒ tan   45 ° = 5 x 1 ,   tan   30 ° = 5 x 2 ⇒ x 1 = 5 ,   x 2 = 5 3 . ⇒ A B = x 1