91Ó°ÊÓ

If the angle of elevation of the sun is \(73.4^{\circ}\) when a building casts a shadow of \(37.5\) feet, what is the height of the building?

Convert each of the following to degrees and minutes. $$ 43.85^{\circ} $$

A tree on one side of a river is due west of a rock on the other side of the river. From a stake \(21.0\) yards north of the rock, the bearing of the tree is \(\mathrm{S} 18.2^{\circ} \mathrm{W}\). How far is it from the rock to the tree?

Change each of the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a degree. $$ 48^{\circ} 27^{\prime} $$

Change each of the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a degree. $$ 78^{\circ} 37^{\prime} $$

A man standing on the roof of a building \(60.0\) feet high looks down to the building next door. He finds the angle of depression to the roof of that building from the roof of his building to be \(34.5^{\circ}\), while the angle of depression from the roof of his building to the bottom of the building next door is \(63.2^{\circ}\). How tall is the building next door?

A ship is anchored off a long straight shoreline that runs north and south. From two observation points 15 miles apart on shore, the bearings of the ship are \(\mathrm{N} \mathrm{} 31^{\circ} \mathrm{E}\) and \(\mathrm{S} \mathrm{} 53^{\circ} \mathrm{E}\). What is the shortest distance from the ship to the shore?

Use a calculator to find each of the following. Round all answers to four places past the decimal point. $$ \cos 24^{\circ} 30^{\prime} $$

For each expression that follows, replace \(x\) with \(30^{\circ}, y\) with \(45^{\circ}\), and \(z\) with \(60^{\circ}\), and then simplify as much as possible. $$ 4 \cos \left(z-30^{\circ}\right) $$

Use a calculator to find each of the following. Round all answers to four places past the decimal point. $$ \csc 48^{\circ} 48^{\prime} $$