SOLUTION: 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

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).

RELATED QUESTIONS
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite... (answered by ankor@dixie-net.com)

Find the lengths of the missing sides if side a is opposite angle A, side b is opposite... (answered by josmiceli,MathTherapy)

For the following exercises, find the lengths of the missing sides if side a is... (answered by Theo,ikleyn)

Find the lengths of the missing sides if side a is opposite angle A, side b is opposite... (answered by Alan3354)

Find the lengths of the missing sides if side a is opposite angle A, side b is opposite... (answered by stanbon)

Use the Law of Sines to solve for the missing side for the oblique triangle. Round your... (answered by math_tutor2020)

Use the figure. Find the lengths of the remaining sides of the triangle. See Example 7.... (answered by MathLover1,MathTherapy)

Use the figure. Find the lengths of the remaining sides of the triangle. See Example 10.... (answered by mananth,MathTherapy)

the sum of the sides of a triangle ABC is 200m.If angle A=37,B=59,and C=84,find the side... (answered by Edwin McCravy)