A vertical pole stands at a point O on horizontal ground. Two observation points A and B are located on the ground such that A is due West of O , and B is due South of O . The angles of elevation of the top of the pole from A and B are 30^ and 60^ respectively. If the distance between points A and B is 200 m , then the height of the pole (in m) is:

Step-by-step solution

Let the height of the vertical pole be h . The point A is due West of O , and the angle of elevation of the top of the pole from A is 30^ . In the right-angled triangle formed by the pole and the ground distance OA : 30^ = h OA OA = h 30^ = h 3 The point B is due South of O , and the angle of elevation from B is 60^ . Similarly: 60^ = h OB OB = h 60^ = h 3 Since A is due West and B is due South of O , the angle AOB on the horizontal ground is 90^ . Applying the Pythagorean theorem in the horizontal right-angled tri