Question

Use the following diagram. Reduce all fractions to lowest terms. Use the / symbol to write the fraction.N2012DA16The trig ratio for Tan N is

Answer 1

The tangent of one of the acute angles of a right triangle is defined as the ratio between the side across the angle (opposite) and the side next to the angle (adjacent)

`\tan \theta=\frac{\text{opposite}}{\text{adjacent}}`

Considering ∠N, the side next to it is side NA, and the side across the angle is DA.

So you can express the tangent of ∠N as follows:

`\tan N=(DA)/(NA)`

We know that DA=16 and NA=12, then the tangent can be calculated as:

`\begin{gathered} \tan N=(16)/(12) \\ \tan N=(4)/(3) \end{gathered}`

The tangent of ∠N is 4/3