91Ó°ÊÓ

A forest ranger sights a fire directly to the south. A second ranger, 7 miles east of the first ranger, also sights the fire. The bearing from the second ranger to the fire is \(\mathrm{S} 28^{\circ} \mathrm{W}\). How far, to the nearest tenth of a mile, is the first ranger from the fire?

A ship sights a lighthouse directly to the south.A second ship, 9 miles east of the first ship, also sights the lighthouse. The bearing from the second ship to the lighthouse is \(S 34^{\circ} \mathrm{W}\). How far, to the nearest tenth of a mile, is the first ship from the lighthouse?

A tower that is 125 feet tall casts a shadow 172 feet long. Find the angle of elevation of the Sun to the nearest degree. (IMAGE CANNOT COPY)

The Washington Monument is 555 feet high. If you are standing one quarter of a mile, or 1320 feet, from the base of the monument and looking to the top, find the angle of elevation to the nearest degree. (IMAGE CANNOT COPY)

A jet leaves a runway whose bearing is \(\mathrm{N} 35^{\circ} \mathrm{E}\) from the control tower. After flying 5 miles, the jet turns \(90^{\circ}\) and files on a bearing of \(\mathrm{S} 55^{\circ} \mathrm{E}\) for 7 miles. At that time, what is the bearing of the jet from the control tower?

A ship leaves port with a bearing of \(\mathrm{S} 40^{\circ} \mathrm{W}\). After traveling 7 miles, the ship turns \(90^{\circ}\) and travels on a bearing of \(\mathrm{N} 50^{\circ} \mathrm{W}\) for 11 miles. At that time, what is the bearing of the ship from port?

A telephone pole is 55 feet tall. A guy wire 80 feet long is attached from the ground to the top of the pole. Find the angle between the wire and the pole to the nearest degree.

A radio station, 98.1 on the \(\mathrm{FM}\) dial, has radio waves with a frequency of 98.1 million cycles per second. Write an equation in the form \(d=\sin \omega t\) for the simple harmonic motion of the radio waves.

Describe one similarity and one difference between the definitions of \(\sin \theta\) and \(\cos \theta,\) where \(\theta\) is an acute angle of a right triangle.

In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\sin 300^{\circ}$$