Question

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

Answer 1

`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'`