tan sin and cos examples, problems

How to punch in tan, cos, sin and the angle:

Press either the angle or the ratio first than the other and the answer comes up usually in a very small number like,  tan20=0.36397023426620236135104788277683

sin20=0.34202014332566873304409961468226

cos20=0.93969262078590838405410927732473

A hiker(b) is looking down at city at a 76 degree angle, what is the distance of the cities length (opposite). say we know the adjacent (1223 ft), and we need to know the length of opposite so the equation for opposite and adjacent is tangent (tan=o/a) so then all we do is tan 76 and multiply that by 1223 which is the adjacent.

Then we get 4905.2 ft as the opposite. Which is the length of the city.  

 (forget 76 as angle for b)Say we dont know angle c but we know each side of the triangle: (ac=10, ab=15, bc=18).  Say that we need to find angle c.  So we can use two of the three terms, tan or sin.  We will use tan so that is the adjacent and the oppoisite of the angle, ac=10 and ab=15.  So the inverse of tan to cancel tan. So the equation to solve it tan-1=15/10 which 56.3.

Now say we dont know the hypotenuse but we have the adjacent side to c, adjacent(10) over hypotanuse would be cos.  The equation would be cos56.3=10/h so to solve we would it be 18.