How do you determine the number of possible triangles and find the measure of the three angles given AB=14, BC=21, mangleC=75?

1 Answer
Bdub
Nov 1, 2017

No Triangle

Explanation:

Since the given information is for a SSA triangle it is the ambiguous case. In the ambiguous case we first find the height by using the formula h=bsin A.

Note that A is the given angle and its side is always a so the other side will be b .

So if A < 90^@ and if

  1. h < a < b then then there are two solutions or two triangles.

  2. h < b < a then there is one solution or one triangle.

  3. a < h < b then there is no solution or no triangle.

If A >=90^@ and if

  1. a > b then there is one solution or one triangle.

  2. a <=b there is no solution

h=21 sin75^@~~20.28, since 14 < 20.28 < 21 we have

a< h < b so we have no solution or no triangle.

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