A vertical tower stands inside a triangular field whose side lengths are 6 m, 8 m, and 10 m. The angles of elevation of the top of the tower from the three corners of the field are all equal to 45^ . The height of the tower is :

Step-by-step solution

Let the foot of the tower be P and its height be h . Since the angles of elevation of the top of the tower from the three corners of the field are equal, the horizontal distances from P to the three corners must be equal. This implies that P is the circumcentre of the triangular field. The sides of the field are 6 m, 8 m, and 10 m. Since 6^2 + 8^2 = 36 + 64 = 100 = 10^2 , the field is a right-angled triangle. For a right-angled triangle, the circumcentre lies at the midpoint of the hypotenuse. Thus, the circumradiu