This here are the three equations possible with sine, cosine, and tangent as well as the three places you could have a variable and you need to find out what the variable is.

for the first equation you have a tangent equation and they’ve already given you the opposite and adjacent and now you have to find out what the variable equals so you have to turn to inverse tangent and divide the opposite over adjacent then multiply inverse tangent with the division you just did. For the cosine equation you have the reference angle and the hypotenuse and they’re asking you to find the adjacent side so what you do is take the reference angle and multiply it with cosine then multiply that with the hypotenuse which should give you the adjacent side. for the third you have a sine equations and they’ve given you the reference angle and the opposite side and the variable is in place of the hypotenuse so what they want you to do is take the opposite side and divide it with sine times 23 which should give you the hypotenuse and you have to always make sure your results make sense and to not concentrate on your illustration of the triangle but only on the information given to you

calculating a sphere versus a hemi-sphere is basically taking a sphere and cutting the calculations in half

for volume you literally take the calculations as you can see from 4/3 there and you cut it in half and you have 4/6 for the hemi-sphere. For surface area it’s not exactly half you just take one off the 4