In the adjoining figure, AP is a man of height 1.8 m and BQ is a building 13.8 m high. If the man sees the top of the building by focussing his binoculars at an angle of 30° to the horizontal, find the distance of the man from the building.

In the adjoining figure, ABC is a triangle in which ∠B = 45° and ∠C = 60°. If AD ⊥ BC and BC = 8m, find the length of the altitude AD.

Without using trigonometric tables, evaluate the following:

$\dfrac{\text{tan 41°}}{\text{cot 49°}}$

Without using trigonometric tables, evaluate the following:

$\dfrac{\text{cosec 17°30}'}{\text{sec 72° 30}'}$.