 In this video we provide the solution to question number 11 for the practice exam number 1 for Math 1060. We're given some triangle diagram that we see right here and we're asked to compute the quantities x and h. So what do we know is there's this white triangle. It's a right triangle which has an angle of 62 degrees. It's adjacent side is the unknown x and the opposite side is the unknown h. There's also this blue right triangle which we see right here. It has an angle of 52 degrees. Its adjacent side is 20 but its opposite side is x. So since the blue triangle has only one unknown and the white triangle has two unknowns we're going to try to solve the blue triangle first. So given that we have opposite over adjacent we're going to use the tangent ratio to solve for x. Notice that tangent of 55 degrees is equal to x over 20. So we can solve for x by times in both sides by 20. We get x is equal to 20 times tangent of 55 degrees. Now be aware that the instructions for this question ask us to compute x and h exactly. So the exact value for x is going to be 20 times the tangent of 55 degrees. So for full credit on this question we do need to include that. If you would like to include an approximation on your calculator you get approximately 28.56. You are welcome to do so but there will be no credit for that approximation even though this question is in the calculator approved section. The exact answer is necessary for full credit. If you had the correct approximation but not the exact answer you wouldn't get full credit. So we found x. Now let's look for h. So looking at the white triangle we know the adjacent side because we solved for x. We want to find the opposite side so let's again do a tangent ratio here. We're going to get that tangent of 62 degrees. This is going to equal h over x which x we now know is 20 times tangent of 55 degrees. Use the exact answer here for now. To solve for h we're going to clear the denominators and so we're going to get h is equal to 20 times tangent of 55 degrees times tangent of 62 degrees. Again for full credit on this question you need the exact answer which would look like this right here. If you want an approximation of h that's okay. You can put it into your calculator and you'll get approximately 53.719 something like that. But you do not need that for full credit with the exact answer you would get full credit. An approximate answer is worth partial credit if the exact answer is not included or is incorrect but the approximation is still correct.