How do you determine the number of possible triangles and find the measure of the three angles given AB=14, BC=21, mangleC=75AB=14,BC=21,m∠C=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 Ah=bsinA.

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

So if A < 90^@A<90∘ and if

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

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

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

If A >=90^@A≥90∘ and if

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

  2. a <=ba≤b there is no solution

h=21 sin75^@~~20.28h=21sin75∘≈20.28, since 14 < 20.28 < 2114<20.28<21 we have

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

Related questions
See all questions in The Ambiguous Case
Impact of this question
2643 views around the world
You can reuse this answer
Creative Commons License