Let M be the projection of T , note that MP is minimum when P lies on A required angle = arc tan TM/MP where tan is an increasing function from 0 to 90 (not include 90)

Let D be the projection point of T on AC so that ∠TPD is the angle of elevation of T from P. ∵ tan ∠TPD = TD / DP As TD keeps constant, ∠TPD is the greatest when DP is the smallest. ∴ DP is the smallest when DP ⊥ AB This means ΔADP is a right-angled triangle with ∠APD = 90⁰, which implies AD is a hypothenuse. Therefore, AD is longer than DP, implying ∠TAD is not the greatest angle of elevation.