Pre-Cal HELP?

Question

I need help with this word problems. Please Help me because I am just not a math person...okay bye :)

A 20 feet Ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. What angle does the ladder make with the ground?


Jon goes to the movies. His seats are 30 feet above stage level. As he watches the angle of depression his line of sight is 15 degrees. How far from the stage is jon?


Gracie flies a kite. The string makes a 57 degree angle of elevation with the ground. If gracie wants to fly a kite 130 feet above the ground, how much string does she need?

Answer 1

This is a right triangle with hypotenuse 20. The base is adjacent to the angle. So cos(x) = base/hypotenuse = 8/20
invcos(x) = .4
x = approx 66.4 degrees

Another triangle. 30 is the opposite. The distance is the hypotenuse.

sin(15) = 30/h
h = 30/sin(15) = 115 feet

130 is the opposite, the string is the hypotenuse

sin(57) = 130/h
h= 130/sin(57) = 155 feet

Try drawing the triangle. It will help you understand what is going on.

Answer 2

For the first question, I assume that the angle the wall makes with the ground is 90 degrees. Let (a) be the angle in question. We get that Cos(a) = 8/20 = .4 So on your calculator (I don't have one with me) use Cos inverse button (with the -1) of .4 and that will give you the angle.

Let (s) be the distance to the stage. So Sin(75) = 30/x
and solving for x we get x = 30/(sin75). Again no calculator.

This last problem is bullshit, it doesn't tell us how tall Gracie is, but assuming they aren't being so picky.....
Let (s) be the amount of string needed. Then Sin57 = 137/x and solving for x gives: x = 137/sin57

The last two problems are basically the same.