Question 1203318: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
sin(B)=1/sqrt(6)
a=5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i get a = 5, b = sqrt(5) and c = sqrt(30).
here's how.
from pythagorus theorem, a^2 + b^2 + c^2
you have a = 5, therefore:
25 + b^2 = c^2
you are given that sin(B) = 1/sqrt(6).
since since(B) = b/c, then you get:
b/c = 1/sqrt(6).
solve for b to get:
b = c/sqrt(6).
in the equation of 25 + b^2 = c^2, raplace b with c/sqrt(6) to get:
25 + (c/sqrt(6))^2 = c^2
simplify to get:
25 + c^2/6 = c^2
subtract c^2/6 from both sides of the equation to get:
25 = c^2 - c^2/6.
multiply both sides of othis equation by 6 to get:
6 * 25 = 6 * c^2 - c^2.
this becomes equal to:
6 * 25 = 5 * c^2
divide both sides of this equation by 5 to get:
6/5 * 25 = c^2
simplify to get:
30 = c^2
solve for c to get:
c = sqrt(30)
you have a = 5 and c = sqrt(30)
since a^2 + b^2 = c^2, you get:
25 + b^2 = 30
solve for b^2 to get:
b^2 = 5
solve for b to get:
b = sqrt(5)
you now have:
a = 5
b = sqrt(5)
c = sqrt(30)
a^2 + b^2 = c^2 becomes 5^2 + sqrt(5)^2 = sqrt(30)^2 which becomes:
25 + 5 = 30 which is true.
a = 5, as given.
sine(b) = sqrt(5) / sqrt(30) = 1/sqrt(6), as given.
it all works out ok.
your solution is:
a = 5, b = sqrt(5), c = sqrt(30).
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