How do you determine the number of possible triangles and find the measure of the three angles given a=8, b=10, mangleA=20?
1 Answer
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
Note that A is the given angle and its side is always a so the other side will be b .
So if
-
h < a < b then then there are two solutions or two triangles. -
h < b < a then there is one solution or one triangle. -
a < h < b then there is no solution or no triangle.
If
-
a > b then there is one solution or one triangle. -
a <=b there is no solution
Now let's use the Law of Cosine
quadratic formula
That is,
To find the measures of angle B we use the law of cosine and solve for B. That is,
and therefore
and therefore