(Problems are excerpts from the source text book)

For the following problems, assume that sides a and b are legs of a right triangle, c is the hypotenuse, and theta is the angle between a and c.
1) theta = 52 degrees, and b = 12. Find a and c.
2) theta = 16 degrees, and c = 12. Find a and b.
3) a = 6, and c = 15. Find b and theta.
4) b = 18, and c = 30. Find a and theta.
5) a = 72, and b = 47. Find c and theta.
6) a = 42, and theta = 72 degrees. Find b and c.

Do the following:
7) The shadow of a flagpole is 50 feet long. A line of sight from the tip of the shadow to the tip of the pole makes an angle of 20 degrees with the ground. How high is the pole?
8) Jill is standing at the top of a vertical cliff and Jack is standing 25 feet away from the foot of the cliff and estimates that the angle of elevation from his position to Jil's is 40 degrees. Approximately how high is the cliff?
9) a) Find the missing entries in the table:

Tan(theta)	0	0.5	1	1.5	2	2.5	3
theta

    b) Plot the above points (x=tan(theta), y=theta), and connect them with a smooth curve (y=arctan(x)).
10) A road up a hill is inclined at 11 degrees to the horizontal. A driver starts driving up this hill and, by checking the odometer, discovers that the steep portion of the road extends for three-quarters of a mile. How much as the car gained in altitude?
11) A javelin is 1 meter long. When it lands after being thrown, it's base is 0.6 meters vertically above the ground. What angle does the javelin make?,br> 12) You must hammer a 3-inch-long nail into a piece of wood "2 inches" thick (1.75 inches, actually). Find the steepest angle at which you can hammer the nail all the way into the wood without it coming out the opposite side.
13) A safety regulation limits the maximum angle of inclination for a ladder on a firetruck of 72 degrees. If a hook-and-ladder firetruck has a ladder that can extend to a length of 90 feet, what is the maximum height that it can reach?