A vertical pole stands at a point O on the horizontal ground. A person at point A , due South of the pole, observes the angle of elevation of the top of the pole to be 60^ . The person then walks a distance of 40 m due East to reach point B , where the angle of elevation of the top of the pole is observed to be 45^ . The height of the pole is:

Step-by-step solution

Let the height of the vertical pole be h . At point A , the angle of elevation is 60^ . The distance from the base of the pole O to A is: OA = h 60^ = h 3 At point B , the angle of elevation is 45^ . The distance from the base of the pole O to B is: OB = h 45^ = h Point A is due South of O , and point B is due East of A . This means the triangle OAB formed on the ground is a right-angled triangle, with the right angle at A . Using the Pythagorean theorem in OAB : OA^2 + AB^2 = OB^2 Substitute the known values ( AB