Question

Consider a right triangle with a side of length x opposite angle A, a side of length y opposite angle B, and a hypotenuse of length z opposite the right angle. If $sinB=1/sqrt(3)$ and x=8, find the length of the other side (y) and the length of the hypotenuse (z).

Answer 1

Answer:

• y = 4√2 ≈ 5.66
• z = 4√6 ≈ 9.80

Step-by-step explanation:

From the sine of the angle, the other trig function values can be determined:

  cos(B) = √(1 -sin²(B)) = √(1 -(1/√3)²) = √(2/3) = (√6)/3

  tan(B) = sin(B)/cos(B) = (1/√3)/(√2/√3) = 1/√2 = (√2)/2

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Then the unknown side can be found from ...

  Tan = Opposite/Adjacent

  tan(B) = y/x

  y = x·tan(B) = 8·√2/2 = 4√2 ≈ 5.66

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And the hypotenuse is ...

  Cos = Adjacent/Hypotenuse

  cos(B) = x/z

  z = x/cos(B) = 8/√(2/3) = 8√(3/2) = 4√6 ≈ 9.80