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sin is opposite over hypotenuse so we know I the length of one leg is 5 and the hypotenuse is 6.

cotangent is adjacent over opposite

we know the opposite is 6. to find the adjacent we use the Pythagorean Theorem.

5 ^ 2 + x ^ 2 = 6 ^ 2
25 + x^2 = 36
x^2 = 11
x = √ 11

now we x is √11, put it over opposite side which is 6.

√11/6
tramserran

Answer: [tex]\frac{\sqrt{11}}{5}[/tex]

Step-by-step explanation:

sin = [tex]\frac{opposite}{hypotenuse}[/tex]

It is given that sin θ = [tex]\frac{5}{6}[/tex]. Use the Pythagorean Theorem to find the length of the adjacent side:

a² + b² = c²

5² + b² = 6²

25 + b² = 36

       b² = 11

      [tex]\sqrt{b^{2}} = \sqrt{11}[/tex]

       b = [tex]\sqrt{11}[/tex]

adjacent =  [tex]\sqrt{11}[/tex], opposite = 5, hypotenuse = 6

cot = [tex]\frac{adjacent}{opposite}[/tex]

      = [tex]\frac{\sqrt{11}}{5}[/tex]

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