SOLUTION: Hi! My problem shows a triangle that has angle A a 21 acute degree angle, sides AC is 13 inches, and is a right triangle. What I have figured out: angle B = 61 degrees and sides

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Question 167929This question is from textbook Algebra 1
: Hi! My problem shows a triangle that has angle A a 21 acute degree angle, sides AC is 13 inches, and is a right triangle.
What I have figured out:
angle B = 61 degrees
and sides CB = 5 inches
What I need:
sides AB
Thank You!
 This question is from textbook Algebra 1

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
If that's a right triangle, then A%2BB%2BC=180%5Eo right?
Since A=21%5Eo in that right triangle C=90%5Eo, then
21%2BB%2B90=180
B=180-90-21
B=69%5Eo
Let's see the triangle below:
---> RED Line AB=unknown?; Blue Line AC=13"; GREEN Line BC=5"
Now, if BC=5, by trigo functions ----> sin%28alpha%29=opp%2Fhyp=BC%2FAB
sin21%5Eo=5%2FAB
AB=5%2Fsin21%5Eo=highlight%2813.952inches=AB%29
Check: Remember in a right triangle:
hyp%5E2=opp%5E2%2Badj%5E2 ---> AB%5E2=BC%5E2%2BAC%5E2
13.952%5E2=5%5E2%2B13%5E2
194.658=25%2B169
194.658%3E=194, close enough, round off.
Thank you,
Jojo