Video Transcript
Using the trigonometric ratios,
find tan of 𝜃.
In this question, we have this
rectangular prism or cuboid, and we can see that 𝜃 is the angle between the line
𝐹𝐷 and 𝐹𝐺. In order to use the trigonometric
ratios, we need to have a right triangle. We could create a right triangle
with the triangle 𝐹𝐷𝐺 and the right angle here at vertex 𝐺. Note that this triangle, 𝐹𝐷𝐺,
would be a two-dimensional triangle as it sits on the face of our cuboid.
It’s often very helpful to draw our
triangles separately so that we can visualize the problem. We’d have vertex 𝐷 at the top and
𝐹 and 𝐺 at the base of this triangle. 𝐷𝐺 is given on the diagram as
four centimeters, and 𝐹𝐺 is three centimeters. The angle 𝜃 is the angle here at
𝐷𝐹𝐺. When we’re 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 we’d have tan of 𝜃 equals the opposite over the adjacent
sides.
The longest side or hypotenuse
isn’t needed for the tan ratio. The side that’s opposite the angle
𝜃 is the length 𝐷𝐺. The side that’s adjacent to our
angle 𝜃 is the length 𝐹𝐺. So we begin by saying that tan 𝜃
equals O over A. That’s opposite over adjacent. And we fill in the lengths that
we’re given. The opposite side is four
centimeters, and the adjacent side is three centimeters. Our answer then for tan 𝜃 is the
fraction four-thirds.
Note that we weren’t actually asked
to calculate the size of the angle 𝜃 but just to find tan 𝜃. If we did want to find the value of
𝜃, we’d need to use the inverse tan function on our calculator.
