This is a free lesson from our course in Trigonometry
In this lesson you'll learn with the help of several examples, practice questions
with solution concepts of the ambiguous case and approach to problem solving. It will
be explained with the help of video presentation and explanation by instructor in
own handwriting. If two sides and an angle opposite to one of them are known, it is called the
ambiguous case. In such a case we may determine more than one triangle or perhaps no triangles at all. The possible solutions
depend on whether the given angle is acute or obtuse. When the Angle is Acute:
Let a, b, and angle B be known, and let B be
acute. Using the Law of Sines,
sin(A) = a sin(B)/b.
In this five different cases exist. (More text below video...)
(Continued from above)When the Angle is Obtuse:
Let a, b, and angle B be known, and let B be
obtuse. Using the Law of Sines,
sin(A) = a sin(B)/b.
In this three different cases exist.
In case of this being right angle, then you can simply use right triangle solving
techniques
Consider the case where two sides of a triangle, say, a and b
and an angle B opposite to the side are given, the height of the triangle
h can be expressed as b sin B i.e.,
h = b sin B.
If a < h, then no triangles can be formed.
If a = h, then only one triangle can be formed.
If h < a < b, then two triangles can be formed
as the side of length a can swing around and form two different triangles.
If a >= b, then only one triangle can be formed.
For example, in triangle ABC if mB
= 64, side a
= 8 cm and b = 12 cm, then plugging the values in h = b
sin B will give h = 10.8. In this case since a (= 8)
< h (= 10.8). Therefore, no triangles can be formed.
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B
= 64
, side a
= 8 cm and b = 12 cm, then plugging the values in h = b
sin B will give h = 10.8. In this case since a (= 8)
< h (= 10.8). Therefore, no triangles can be formed.