 In this video, we provide the solution to question number 10 for the practice exam number one for math 1060 We're given a right triangle diagram listed as so one of the interior angles is 30 degrees It's adjacent side is some unknown quantity x and the hypotenuse of this right triangle is 10 And we are asked to compute the number x for this situation right here And also be aware that we are not allowed to use a calculator on this question So we're gonna have to remember the trigonometry of a 30 30 degree angle and a right triangle in fact if this angle is 30 degrees that means this angle right here is 60 degrees So this really is a 30 60 90 triangle so if you wanted to since we didn't know the adjacent side and The hypotenuse you could do a cosine ratio We could say that cosine of 30 degrees is equal to x over 10 For which you could clear the total errors and get x equals 10 times cosine of 30 degrees So then we have to remember that cosine of 30 degrees is equal to root 3 over 2 2 goes into 10 5 times you get 5 root 3 So that would be an appropriate way to solve this one getting choice F Another possibility you could see here is that with a 30 60 90 triangle the short side Which is the side opposite of the 30 degree angle is always half of the hypotenuse So you can very quickly get that this distance here is 5 and then to get to the side opposite of the 60 degree angle in a 30 60 90 triangle you take the short side You times it by the square root of 3 which would also give you 5 times square 3 So two different strategies for solving the same question Ultimately though, we do need to know the trigonometry of a 30 60 90 triangle since you do not have access to a calculator on this question