A pole stands vertically inside a triangular park
ABC. If the angle of elevation of the top of the
pole from each corner of the park is same, then
the foot of the pole is at the
(a) centroid (b) circumcentre
(c) incentre (d) orthocentre
ABC. If the angle of elevation of the top of the
pole from each corner of the park is same, then
the foot of the pole is at the
(a) centroid (b) circumcentre
(c) incentre (d) orthocentre
Answers & Comments
Verified answer
Answer:
In the given problem, we have a triangular park ABC, and there is a pole standing vertically inside the park. The angle of elevation of the top of the pole from each corner of the park is the same. Let's analyze the possible positions for the foot of the pole:
(a) Centroid (b) Circumcentre (c) Incentre (d) Orthocentre
1. Centroid (a): The centroid of a triangle is the point where the medians of the triangle intersect. The medians connect each vertex to the midpoint of the opposite side. Placing the pole at the centroid would mean that the pole divides each median into two equal segments. This scenario doesn't ensure that the angles of elevation from each corner are the same. So, it's not the correct answer.
2. Circumcentre (b): The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. Placing the pole at the circumcentre would mean that the pole is equidistant from all three corners of the park. This doesn't guarantee that the angles of elevation from each corner are the same. So, it's not the correct answer.
3. Incentre (c): The incentre of a triangle is the point where the angle bisectors of the triangle intersect. Placing the pole at the incentre would mean that the pole is equidistant from all three sides of the park. This also doesn't ensure that the angles of elevation from each corner are the same. So, it's not the correct answer.
4. Orthocentre (d): The orthocentre of a triangle is the point where the altitudes of the triangle intersect. Placing the pole at the orthocentre would mean that the pole is on one of the altitudes of the triangle. If the pole is positioned in such a way that it is equidistant from all three corners and along one of the altitudes, then the angles of elevation from each corner will indeed be the same. So, the correct answer is (d) Orthocentre.
Therefore, to have the same angle of elevation from each corner of the triangular park, the foot of the pole should be at the orthocentre of the triangle.
Step-by-step explanation:
If the angle of elevation of the top of the pole from each corner of the triangular park is the same, it means that the pole's top is equidistant from each corner of the park, forming an equilateral triangle with the park's vertices. In this case, the foot of the pole is at the centroid of the triangular park.
So, the correct answer is (a) centroid.