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In right triangle \(ABC\), shown below, \(\cos{B}=\frac{6}{10}\). What is \(\tan{C}\)?

 Dec 14, 2021
 #1
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$\tan C = \boxed{\frac{5}{4}}$.

 Dec 14, 2021
 #3
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Be careful. The hypotenuse is not a side.

tinfoilhat  Dec 14, 2021
 #2
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The definition of cosine is the opposite side of the angle divided by the hypotenuse. This means that AC/10 = 6/10, so AC = 6. By the Pythagorean theorem, AB = √(10^2-6^2) = 8.

The tangent's definition is the side opposite to the angle divided by the side adjacent to the angle. This is AC/AB = 6/8 = 3/4.

 Dec 14, 2021

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