Solve SAA or ASA Triangles Solve SSA Triangles Solve Applied Problems The Law of Sines Solve SAA or ASA Triangles Solve SSA Triangles Solve Applied Problems

Triangles An oblique triangle is a triangle that does not have a right angle. It can have either three acute angles or two acute angles and one obtuse angle To solve an oblique triangle means to find the lengths of its sides and the measurement of its angles

How to solve an oblique triangle We need to know Case 1: One side and two angles are known (ASA or SAA) Case 2: Two sides and the angle opposite one of them are known (SSA) Case 3: Two sides and the included angle are known Case 4: Three sides are known (SSS)

The Law of Sines The Law of Sines is used to solve triangles for which Case 1 or 2 holds (ASA, SAA, SSA) Law of Sines: For a triangle with sides a, b, c and opposite angles α, β, γ, respectively

Using the law of Sines Solve the triangle: α=40° β= 60 a= 4

The Ambiguous Case Case 2 (SSA) is referred to the ambiguous case, because the known information may result in one triangle, two triangles or no triangles at all. The key to determining the possible triangles, if any that may be formed from the given information lies primarily with the height h and the fact that h=b sin α

No Triangle If a < h = b sin α then side a is not sufficiently long enough to form a triangle

No Solution Solve the triangle: a=2, c=1, and γ= 50°

One Solution Solve the triangle: a = 3 b=2 α= 40°

Two Solutions Solve the triangle: a=6, b=8 and α= 35 °

Finding the Height of a Mountain To measure the height of a mountain, a surveyor takes two sightings of the peak at a distance 900 meters apart on a direct line to the mountain. The first observation results in an angle of elevation of 47° whereas the second results in an angle of elevation of 35°. If the transit is 2 meters high, what is the height h of the mountain?

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