Second Method: Take 1/3 tabular difference.
sin 21 13' = 0.36190
sin 21 12' = 0.36162
So: 1/3 (0.00028) = 0.00009
Therefore: sin 21€ 12' = 0.36162
1/3 tabular difference = 0.00009
Then: sin 21 12' 20" = 0.36171
g. It must be remembered that the tabular values of the sine and tangent increase as the size of
the angle increases, and the tabular values of the cosine and cotangent decrease as the size of the angle
increases. To avoid confusion and errors in interpolation, it is advisable to follow the methods used
above, adding the proportional parts for seconds in the case of sines and tangents and subtracting the
proportional parts in the case of cosines and cotangents.
h. As you will recall, the triangle has six parts: three angles (one of which is 90€) and three
sides (see Figure 4-6, page 4-14). If two sides, or one side and an acute angle, are given, you can
compute the unknown parts of the triangle. This computation is called the solution of a triangle. From
this statement, it is evident that in order to solve a right triangle, two parts besides the right angle must
be given, at least one of them being a side. The two given parts may be-
An acute angle and the opposite leg.
An acute angle and the adjacent leg.
The two legs.