91Ó°ÊÓ

The CN Tower in Toronto, Canada, is the tallest free-standing structure in North America. A woman on the observation deck, 1150 ft above the ground, wants to determine the distance between two landmarks on the ground below. She observes that the angle formed by the lines of sight to these two landmarks is \(43^{\circ} .\) She also observes that the angle between the vertical and the line of sight to one of the landmarks is \(62^{\circ}\) and that to the other landmark is \(54^{\circ} .\) Find the distance between the two landmarks. (IMAGE CAN'T COPY)

A laser beam is to be directed toward the center of the moon, but the beam strays \(0.5^{\circ}\) from its intended path. (a) How far has the beam diverged from its assigned target when it reaches the moon? (The distance from the earth to the moon is \(240,000\) mi.) (b) The radius of the moon is about \(1000 \mathrm{mi}\). Will the beam strike the moon?

From the top of a 200 -ft lighthouse, the angle of depression to a ship in the ocean is \(23^{\circ} .\) How far is the ship from the base of the lighthouse?

If two triangles are similar, what properties do they share? Explain how these properties make it possible to define the trigonometric ratios without regard to the size of the triangle.

The wheels of a car have radius 11 in. and are rotating at 600 rpm. Find the speed of the car in \(\mathrm{mi} / \mathrm{h}\).

A truck with 48 -in.-diameter wheels is traveling at \(50 \mathrm{mi} / \mathrm{h}\). (a) Find the angular speed of the wheels in rad/min. (b) How many revolutions per minute do the wheels make?