Question

How do you solve the right triangle ABC given A= 20 degrees C= 104 degrees and c=9?

Answer 1

`/_B = 180^o -( 20^o + 102^o) = 56^0`
Using the Law of Sines
`color(white)("XXXX")` `a = 3.172416`
`color(white)("XXXX")` `b= 7.689757`

Explanation:

Ignoring the fact that the question declared that the triangle was a right triangle (obviously impossible with one angle = `102^o`):

The third angle can be calculated using the knowledge that the sum of the interior angles of any triangle is always `180^o`.

Using the Law of Sines in the form:
`color(white)("XXXX")` `c/sin(C) = a/sin(A) = b/sin(B)`
we can calculate (for example):
`color(white)("XXXX")` `a = sin(A)*c/sin(C) = sin(20^o)*9/sin(102^o)`
and through the magic of hand calculators or spreadsheet functions come up with the indicated answers.