Question

how do I use a sketch to find the exact value of the problem in the image? I know the answer is 12/5 ( i think) but I don't know how to specifically represent it to find it in a sketch.

Answer 1

In the right triangle, there are 2 legs of the right angle and one hypotenuse (the side opposite to the right angle

The ratio cos(x) = adjacent side to the angle x/ hypotenuse

Then if cos(x) = 5/13, then

That means the adjacent side to angle x = 5 and the hypotenuse = 13

Let us draw the sketch

To find tan we have to find the other leg of the right angle which is opposite to angle x

We will use the Pythagoras Theorem

`\begin{gathered} L=\sqrt[]{13^2-5^2} \\ L=\sqrt[]{169-25} \\ L=\sqrt[]{144} \\ L=12 \end{gathered}`

Since tan(x) = opposite side to x/ adjacent side to x

Since the opposite side is 12

Since the adjacent side is 5, then

`\begin{gathered} \tan (x)=(12)/(5) \\ \tan (\cos ^(-1)(5)/(13))=(12)/(5) \end{gathered}`