### Video Transcript

Find the length π΄π΅, giving your answer to two decimal places.

The length π΄πΆ in the diagram is 39 centimetres. And the angle π΅π΄πΆ is equal to 37 degrees. As the triangle is right-angled, we can solve this problem using the trigonometrical ratios. Sin π is equal to the opposite divided by the hypotenuse. Cos π is equal to the adjacent divided by the hypotenuse. And tan π is equal to the opposite divided by the adjacent.

In this example, weβre looking to calculate the length π΄π΅, labelled π₯ on the diagram. The length π΄πΆ is the hypotenuse of the triangle as it is the longest side and itβs opposite the right angle. π΅πΆ is the opposite as it is opposite the 37-degree angle. And π΄π΅ is the adjacent as it is next to or adjacent to the 37- and 90-degree angles.

As we are going to use the adjacent and the hypotenuse, weβll use the cosine ratio. Cos π equals the adjacent divided by the hypotenuse. Substituting in our values from the diagram gives us cos 37 is equal to π₯ divided by 39. Multiplying both sides of this equation by 39 gives us 39 multiplied by cos 37 is equal to π₯. This gives a value of π₯ of 31.15. This means that the length of π΄π΅ is 31.15 centimetres to two decimal places.