# Question Video: Understanding the Tangent Ratio Mathematics • 11th Grade

In the given figure, ๐โ ๐ต๐ด๐ถ = 90ยฐ and ๐ด๐ท โฅ ๐ต๐ถ. What is ๐ด๐ถ tan ๐?

02:16

### Video Transcript

In the given figure, the measure of angle ๐ต๐ด๐ถ is equal to 90 degrees and the line ๐ด๐ท is perpendicular to ๐ต๐ถ. What is ๐ด๐ถ tan ๐?

So in this question, weโve got a right-angle triangle cause weโre told that the measure of angle ๐ต๐ด๐ถ is equal to 90 degrees. So thatโs a right angle. So therefore, because weโve got a right-angle triangle, we know that we can have a look at the trigonometric ratios. And when weโre 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, weโre looking for ๐ด๐ถ tan ๐. Well therefore, we know that weโre gonna be interested in TOA because thatโs 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 weโre gonna label is our hypotenuse. And thatโs because this is the side thatโs opposite the right angle. And itโs also the longest side of our triangle. And the triangle weโre interested in is the triangle ๐ด๐ต๐ถ. Now, the next side weโre 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 thatโs next to the angle ๐ and also between the angle ๐ and the right angle.

So in this question, weโre interested in the opposite and the adjacent because weโre 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 ๐ด๐ต, the opposite, divided by ๐ด๐ถ, which is the adjacent. And then, what we can do is multiply each side of the equation by ๐ด๐ถ to remove it from the denominator so to get rid of the fraction.

And when we do that, we get ๐ด๐ถ tan ๐ is equal to ๐ด๐ต. So that solved the problem because what we were looking for is what ๐ด๐ถ tan ๐ was. And ๐ด๐ถ tan ๐, as weโve already said, is ๐ด๐ต.