From the top of a vertical cliff 20m high, a boat at sea can sighted 75 m away and on the same horizontal position as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff

If $\tan x=\frac{3}{4}$, $0{}^\circ <x<90{}^\circ $evaluate $\frac{\cos x}{2\sin x}$

The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8 m above the ground. How long is the ladder 

In $\Delta XYZ$, $\left| YZ \right|=32cm$, $\angle YXZ=52{}^\circ $ and $\angle XZY=90{}^\circ $ Find, correct to the nearest centimetre, $\left| XZ \right|$

Given that Y is 20m on a bearing of 300^o from X, how far south of Y is X?

If $\tan x=\tfrac{4}{3}$, $0{}^\circ <x<90{}^\circ $, find the value of $\sin x-\cos x$ 

The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot on the tree is 30^o. Find the height of the tree.

A stationary boat is observed from a height of 100 m . If the horizontal distance between the observer and the boat is 80 m. Calculate, correct to two decimal places, the angle of depression of the boat from the point of observation

Given that$\cos {{30}^{\circ }}=\sin {{60}^{\circ }}=\frac{\sqrt{3}}{2}$ and $\sin {{30}^{\circ }}=\cos {{60}^{\circ }}=\frac{1}{2}$ evaluate $\frac{\tan {{60}^{\circ }}-1}{1-\tan {{30}^{\circ }}}$ 

A bearing of 320^o expressed as a compass bearing is