Download Law of Sines

SOH-CAH-TOA
Here's a quick recap of how to set up the trig ratios.
Special Right Triangles
45.45.90
30.60.90
TIPS IN SOLVING FOR RIGHT TRIANGLES: meaning find all measures of side lengths and angles of the
triangle.
Right Triangles
If you are given:
two legs
leg and hypotenuse
angle and hypotenuse
Then begin by using:
tangent
sine or cosine
sine or cosine
Solving for angles
Inverse functions
Any Triangle
If you are given:
two angles and any side
two sides and the angle opposite one of them
Then begin by using:
Law of Sines
Law of Sines
ANGLES OF ELEVATION AND DEPRESSION:
Problems that involve looking up to an object can be described in terms of an angle of elevation -- the angle between an
observer's line of sight and a horizontal line. In this example, the passenger on the ship looking straight ahead would
have to raise (elevate) his eyes to see the airplane above.
When an observer is looking down, the angle of depression is the angle between the observer's line of sight and a
horizontal line. In this example, the pilot of the airplane looking straight ahead would have to lower (depress) his eyes to
see the ship below.
If you think of the two horizontal lines of sight as being parallel to each other, then you will realize that the angles of
depression and elevation are alternate interior angles and therefore are congruent to each other.
Law of Sines
In a triangle, there is a relationship between the angles of the triangle and the lengths of the sides opposite these angles.
The Law of Sines can be used to find the measures of missing parts if the following conditions are true:

AAS or ASA You know the measures of two angles and any side of the triangle.

SSA You know the measures of two sides and an angle that is opposite one of these sides of the triangle.
Theorem
Let triangle ABC be any triangle with a, b, and c representing the measures of the sides opposite the angles with
measures A, B, and C, respectively. Then the ratios of these angles to the lengths of the opposite sides will be equal to
each other -- sin A : a = sin B : b = sin C : c.
The Law of Sines can be used to solve a triangle if you know the measures of two angles and any side of a triangle, or if
you know the measures of two sides and an angle opposite one of these sides of the triangle.
You use the Law of Sines to write a proportion. You cross multiply and solve for your missing part.