SOLUTION: Solve the right triangle with the given sides and angles. a= 3.0 A= 31.0°

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Question 929644: Solve the right triangle with the given sides and angles.
a= 3.0
A= 31.0°
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:the right triangle
a=+3.0
A=alpha=+31.0°=> B=beta=+90-31.0°=> beta=+59.0°
to find side b we can use the definition:
tan%28angle%29=opposite_leg%2Fadjacent_leg
In this case we have:
tan%28alpha%29=a%2Fb
After substituting alpha=31 and a=3 we have:
tan%2831%29=3%2Fb
b=3%2Ftan%2831%29%0D%0A%0D%0A%7B%7B%7Bb=3%2F0.6009
b=4.99
and, now we can use Pythagorean theorem to find side c

c%5E2=a%5E2%2Bb%5E2
c%5E2=3%5E2%2B%284.99%29%5E2
c%5E2=9%2B24.9
c%5E2=33.9
c=sqrt%2833.9%29
c=5.82