A vertical pole stands inside a triangular park with side lengths 13 m, 14 m, and 15 m. The angles of elevation of the top of the pole from the nearest point on each of the three sides of the park are all equal to 30^ . The height of the pole is :

Step-by-step solution

Let the foot of the pole be P and its height be h . The angles of elevation of the top of the pole from the nearest point on each of the three sides are equal. The nearest point on a side is the foot of the perpendicular drawn from P to that side. Since the angles of elevation are equal, the perpendicular distances from P to the three sides must be equal. This implies that P is the incentre of the triangular park, and the horizontal distance to each side is the inradius r . The sides of the park are a = 13 m, b = 1