### Video Transcript

In the given figure, the measure of
angle ๐ต๐ด๐ถ is equal to 90 degrees and the line ๐ด๐ท is perpendicular to ๐ต๐ถ. What is ๐ด๐ถ tan ๐?

So in this question, weโve got a
right-angle triangle cause weโre told that the measure of angle ๐ต๐ด๐ถ is equal to
90 degrees. So thatโs a right angle. So therefore, because weโve got a
right-angle triangle, we know that we can have a look at the trigonometric
ratios. And when weโre dealing with the
trigonometric ratios, we have a memory aid, which is SOHCAHTOA. And what this does is it tells us
how to work out sin ๐, cos ๐, and tan of ๐.

In this question, weโre looking for
๐ด๐ถ tan ๐. Well therefore, we know that weโre
gonna be interested in TOA because thatโs the one that deals with the tangent
ratio. And what TOA tells us that we said
is that tan ๐ is equal to the opposite divided by the adjacent. So what do we do now? Well, the next step is to label our
triangle.

Well, the first side that weโre
gonna label is our hypotenuse. And thatโs because this is the side
thatโs opposite the right angle. And itโs also the longest side of
our triangle. And the triangle weโre interested
in is the triangle ๐ด๐ต๐ถ. Now, the next side weโre gonna
label is the opposite because this is the side opposite the angle, which is ๐. And the final side is the
adjacent. And this is the side thatโs next to
the angle ๐ and also between the angle ๐ and the right angle.

So in this question, weโre
interested in the opposite and the adjacent because weโre dealing with tan ๐. So therefore, if we substitute
these into our formula for tan ๐, we can see that tan ๐ is equal to ๐ด๐ต, the
opposite, divided by ๐ด๐ถ, which is the adjacent. And then, what we can do is
multiply each side of the equation by ๐ด๐ถ to remove it from the denominator so to
get rid of the fraction.

And when we do that, we get ๐ด๐ถ
tan ๐ is equal to ๐ด๐ต. So that solved the problem because
what we were looking for is what ๐ด๐ถ tan ๐ was. And ๐ด๐ถ tan ๐, as weโve already
said, is ๐ด๐ต.