Consider the following for the next two (02) items that follow: The perimeter of a triangle ABC is 6 times the AM of sine of angles of the triangle. Further BC=3 and CA=1.
Consider the following for the next two (02) items that follow: In a triangle PQR, P is the largest angle and cosP=31. Further the in-circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively such that the lengths PN, QL and RM are n, n+2, n+4 respectively where n is an integer.
The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b.