Question

A sign-post in the form of an isosceles triangle ABC is mounted on a pole of height h fixed to the ground. The base BC of the triangle is parallel to the ground. A man standing on the ground at a distance d from the sign-post finds that the top vertex A of the triangle subtends an angle β and either of the other two vertices subtends the same angle α at his feet. Find the area of the triangle.

Answer 1

Let ABC be isosceles triangle mounted on the pole PD and O be the position of the man on the ground so that AD = H. 

Angles α and β are the angles subtended by the vertex C and Δ at O respectively. CQ is parallel to DP so that CQ=h and then PQ = a