How do you determine the number of possible triangles and find the measure of the three angles given a=9, c=10, mangleC=150a=9,c=10,m∠C=150?

1 Answer
Bdub
Oct 31, 2017

A=26^@45', B=150^@, C=3^@15'

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=9 sin150^@=4.5, since 4.5 < 9 < 10 we have

h < b < a so we are looking for one solution. Hence,

Sin A/a = sin B / b

sin A /9 = sin 150^@/10

sin A =(9 sin 150^@)/10

A=sin^-1 ((9 sin 150^@)/10)=26^@45'

and therefore

C=180^@-150^@-26^@ 45'=3^@15'

Related questions
See all questions in The Ambiguous Case
Impact of this question
2589 views around the world
You can reuse this answer
Creative Commons License