### Video Transcript

In the given figure, find the length of ๐ด๐ถ to two decimal places.

Our first step here is to let the length ๐ด๐ถ equal ๐ฅ. We can next label our triangle and use right angle trigonometry to work out the missing length. Right angle trigonometry involves the sine, cosine, and tangent ratios often known as SOHCAHTOA.

The length ๐ด๐ถ is the hypotenuse as it is the longest side and is opposite the right angle. The length ๐ด๐ต is the opposite as it is opposite the 40-degree angle we will be working with. Finally, the length ๐ต๐ถ is the adjacent as it is adjacent or next to the 40-degree angle and the right angle. We know the length of the adjacent. And weโre trying to calculate the hypotenuse. This means that we will use the cosine ratio.

The cosine ratio states that cos ๐ is equal to the adjacent divided by the hypotenuse. Substituting in the values from our diagram gives us cos 40 is equal to five divided by ๐ฅ. Multiplying both sides of this equation by ๐ฅ and then dividing by cos 40 means that the cos 40 and ๐ฅ will in effect swap places. This means that ๐ฅ is equal to five divided by cos 40.

At this stage, itโs important to remember that the hypotenuse was the longest side. Therefore, our answer needs to be greater than five. Typing five divided by cos 40 into our calculator gives us an answer of 6.5270 and so on.

We were asked to give our answer to two decimal places. This means that our answer must have two numbers after the decimal point. The deciding number is the seven. And as this is greater than five, we will round up. ๐ฅ is therefore equal to 6.53 to two decimal places.

As ๐ฅ was the length ๐ด๐ถ on the triangle, we can say that ๐ด๐ถ is equal to 6.53. Thereโre no units in this question. But this could be any units of length, for example, centimeters or meters.