91Ó°ÊÓ

Evaluate, correct to 4 decimal places: (a) secant \(5.37\) (b) cosecant \(\pi / 4\) (c) cotangent \(\pi / 24\) (a) Again, with no degrees sign, it is assumed that \(5.37\) means \(5.37\) radians. Hence \(\sec 5.37=\frac{1}{\cos 5.37}=1.6361\) (b) \(\operatorname{cosec}(\pi / 4)=\frac{1}{\sin (\pi / 4)}=\frac{1}{\sin 0.785398 \ldots}\) \(=1.4142\) (c) \(\cot (5 \pi / 24)=\frac{1}{\tan (5 \pi / 24)}=\frac{1}{\tan 0.654498 \ldots}\) \(=1.3032\)

A surveyor measures the angle of elevation of the top of a perpendicular building as \(19^{\circ}\). He moves \(120 \mathrm{~m}\) nearer the building and finds the angle of elevation is now \(47^{\circ}\). Determine the height of the building.

The angle of depression of a ship viewed at a particular instant from the top of a \(75 \mathrm{~m}\) vertical cliff is \(30^{\circ}\). Find the distance of the ship from the base of the cliff at this instant. The ship is sailing away from the cliff at constant speed and one minute later its angle of depression from the top of the cliff is \(20^{\circ}\). Determine the speed of the ship in \(\mathrm{km} / \mathrm{h}\).

A vertical aerial stands on horizontal ground. A surveyor positioned due east of the aerial measures the elevation of the top as \(48^{\circ}\). He moves due south \(30.0 \mathrm{~m}\) and measures the elevation as \(44^{\circ}\). Determine the height of the aerial.