how do you find which ratio in trig. to use?

Question

HELPPPPPPPPPP!

Answer 1

Some examples:

You are given the distance (along the ground) between Joe and a tower , and you are told the angle his line of sight with the top of the tower makes with the ground (the angle of elevation). You want to find the height of the tower.

Draw a right triangle. You want to know the side OPPOSITE the given angle, and you are told the length of the side
ADJACENT to the given angle, so you use tangent.

If you were given the line-of-sight distance from Joe to the top of the tower instead of the distance along the ground, (but are given the same angle information and still want to find the height of the tower) then you are given the hypotenuse and want to know the opposite side, so you would use sine.

If you are given the distance along the ground and want to know the line-of-sight distance (again with the same angle information), then you are given the adjacent side and want to find the hypotenuse, so you would use cosine.

In general:
1) draw a picture
2) label the angle you know, inside the triangle
3) identify the length being asked for as opp, adj, or hyp, and label that side in the diagram with "x" or some variable name
4) identify the length that is given as opp, adj, or hyp., and label that side of the triangle with the given number
5) the problem now solves itself!

Answer 2

It depends on what data you are given and what you need to find.

Beyond that, you often have a choice of which function to use because the trig functions are interrelated. Different path, same destination.

Answer 3

sin(x) = opp/hyp

cos(x) = adj/hyp

tan(x) = opp/adj

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = 1/tan(x)