Download GUIDELINES FOR SOLVING TRIANGLES

GUIDELINES FOR SOLVING TRIANGLES
1) For right triangles, use “regular” trigonometry, inverse-trig, and the Pythagorean Theorem.
2) For AAS or ASA, use Law of Sines to find both missing sides.
3) For SSA, use the Ambiguous Case of the Law of Sines to find a missing angle, followed by the
missing side.
a)
b)
c)
If the side opposite the given angle is shorter than the height opposite that angle
or if your first step with Law of Sines renders no solution (sine > 1), you will have no
triangles. If you are given an obtuse angle, and the side opposite this angle is not
the longest side of the triangle, you will also realize that you have no triangles. If
there is at least one triangle, proceed to (b) and (c).
If the side opposite the given angle is shorter than the other given side and, in your
first step with Law of Sines, the solution angle’s supplement and the given angle
add to less than 180°, you will have two triangles. (A given obtuse angle renders
this scenario impossible.) Continue to solve both triangles.
If the side opposite the given angle is longer than the other given side or, in your
first step with Law of Sines, the solution angle’s supplement and the given angle
add to be greater than 180°, you will have one triangle. Continue to solve it.
4) For SSS or SAS, use Law of Cosines.
a) For SSS, solve for the largest angle first. Then, use Law of Sines to find a second angle.
b) For SAS, solve for the missing side first.
i)
Then, if you know that the largest angle is given, use Law of Sines to find a second
angle.
ii) Then, if you do not know that the largest angle is not given, use Law of Cosines to find a
second angle.
*For any triangle in which you know two angle measures, you can subtract these from 180° to find the
third angle measure.