Question

In a right triangle, what do you call the ratio of the lengths of the adjacent side of an acute angle to the opposite side?

Answer 1

Answer:

The ratio of the lengths of the adjacent side of an acute angle to the opposite side is cotangent (option C)

Step-by-step explanation:

`\begin{gathered} Ratio\text{ of length of adjacent side to the opposite side = }(adjacent)/(opposite) \\ We\text{ need to find the trigonometry with this formula from the option} \end{gathered}`

In trigonometry SOHCAHTOA, the common ratio ratios are:

`\begin{gathered} sin\text{ = }(opposite)/(hypotenuse) \\ cos\text{ = }(adjacent)/(hypotenuse) \\ tan\text{ = }(opposite)/(adjacent) \end{gathered}`

From the above, the inverse of the tan ratio will give adjacent/opposite

`\begin{gathered} (1)/(tan)\text{ = }(1)/((opposite)/(adjacent)) \\ (1)/(tan)\text{ = }(adjacent)/(opposite) \\ \\ Recal\text{ in trigonometry, }\frac{1}{tan\text{ }}\text{ = cot } \end{gathered}`
`\begin{gathered} As\text{ a result, cot = }(adjacent)/(opposite) \\ Cot\text{ means cotangent.} \end{gathered}`

The ratio of the lengths of the adjacent side of an acute angle to the opposite side is cotangent (option C)