Here is a trig table based on a circle of radius 200. Angles are given in degrees. You can tell that the circle is of radius 200 because the table gives sin 90 as 200.
Angle 
Sin 
Tan 
Sec 
0 
0 
0 
200 
10 
35 
35 
203 
20 
68 
73 
213 
30 
100 
115 
231 
40 
129 
168 
261 
45 
141 
200 
283 
50 
153 
238 
311 
60 
173 
346 
400 
70 
188 
549 
585 
80 
197 
1134 
1152 
90 
200 


1. How does sin 90 = 200 tell you that the circle is of radius 200?
2. How can you use this table to get our modern value of sin 45, which we know to be about 0.701?
3. How can you use this table to get cosines?
4. In this table, is it still true that tan x = (sin x)/(cos x)? How about sec x = 1/cos x? Why or why not?
5. Suppose ABC is a right triangle with right angle at C, and that sides a, b, c are opposite angles A, B, C, respectively. If b = 25 and if A = 40°, then use the table to find the length of side a. You should not convert to modern values of sine and cosine. In fact, it is better if you do not use any decimals, only fractions and whole numbers.
6. Suppose that ABC is a right triangle, with A = 20° and c = 40. Find a.