### Video Transcript

Using the trigonometric ratios,
find tan of ๐.

In this question, we have this
rectangular prism or cuboid, and we can see that ๐ is the angle between the line
๐น๐ท and ๐น๐บ. In order to use the trigonometric
ratios, we need to have a right triangle. We could create a right triangle
with the triangle ๐น๐ท๐บ and the right angle here at vertex ๐บ. Note that this triangle, ๐น๐ท๐บ,
would be a two-dimensional triangle as it sits on the face of our cuboid.

Itโs often very helpful to draw our
triangles separately so that we can visualize the problem. Weโd have vertex ๐ท at the top and
๐น and ๐บ at the base of this triangle. ๐ท๐บ is given on the diagram as
four centimeters, and ๐น๐บ is three centimeters. The angle ๐ is the angle here at
๐ท๐น๐บ. When weโre using the trigonometric
ratios, we often use the phrase SOH CAH TOA to help us remember them. The TOA part helps us to remember
tan of the angle, so weโd have tan of ๐ equals the opposite over the adjacent
sides.

The longest side or hypotenuse
isnโt needed for the tan ratio. The side thatโs opposite the angle
๐ is the length ๐ท๐บ. The side thatโs adjacent to our
angle ๐ is the length ๐น๐บ. So we begin by saying that tan ๐
equals O over A. Thatโs opposite over adjacent. And we fill in the lengths that
weโre given. The opposite side is four
centimeters, and the adjacent side is three centimeters. Our answer then for tan ๐ is the
fraction four-thirds.

Note that we werenโt actually asked
to calculate the size of the angle ๐ but just to find tan ๐. If we did want to find the value of
๐, weโd need to use the inverse tan function on our calculator.