Question

Write each ratio using the given figure. If necessary, find the missing side.Tan P = ___________Answer?

Answer 1

Hello!

First, let's analyze the figure and write each side:

Analyzing it, we don't have enough information yet to calculate the tangent (because we don't know the measurement of P).

So, let's calculate the opposite side (by Pithagoras):

`\begin{gathered} a^2=b^2+c^2 \\ 41^2=40^2+c^2 \\ 1681=1600+c^2 \\ 1681-1600=c^2 \\ c^2=81 \\ c=√(81) \\ c=9 \end{gathered}`

As we know the opposite side, we can calculate the tangent of P, look:

`\begin{gathered} \tan(P)=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \tan(P)=(9)/(40) \\ \\ \tan(P)=0.225 \end{gathered}`

Curiosity: using the trigonometric table, this value corresponds to approximately 13º.

Answer:

The tangent of P is 0.225.