Trigonometry help?

Question

I am in Algebra 3-4/Trig and i need some answers with work shown

so if you could answers these problems and show your work as best as possible ( i know its hard on the computer but try please)

1. arcsin(√3/2)

2.arctan(1/√3)

3.
A=80 a=10
B=60 b=?
C=? c=?

4.
A=? a=8
B=? b=17
C=? c=7

5. Find the area a=8 b=3 c=12
6. find the area B=72 a=25 c=30

Answer 1

The first two problems are easily solved by sketching a unit circle along with the appropriate values. The first is 60 degrees; the second is 30 degrees.
Third problem: law of sines trivially gives b. If A+B = 140, then C = 40, and c can be calculated.
Fourth problem: no solution. Since b > a+c, no triangle can be made.
Fifth problem: also no solution; same reason.
Sixth problem: There is a formula in your trig book for calculating the third side. Once you have that, you can get the missing angles. Now drop a perpendicular from any point to the opposite side; the resulting right triangle can be solved easily to get the altitude.

Answer 2

al the solution for 2 are 60+2k*360 and 120 deg+2k360 degrees
Between 0 and 360 we have 60 and 120 degrees
2) 30deg and 210 degrees