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)

Explanation:

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

In trigonometry SOHCAHTOA, the common ratio ratios are:

$\begin{gathered} sin\text{ = }\frac{opposite}{hypotenuse} \\ cos\text{ = }\frac{adjacent}{hypotenuse} \\ tan\text{ = }\frac{opposite}{adjacent} \end{gathered}$

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

$\begin{gathered} \frac{1}{tan}\text{ = }\frac{1}{\frac{opposite}{adjacent}} \\ \frac{1}{tan}\text{ = }\frac{adjacent}{opposite} \\ \\ Recal\text{ in trigonometry, }\frac{1}{tan\text{ }}\text{ = cot } \end{gathered}$$\begin{gathered} As\text{ a result, cot = }\frac{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)