Second Method: Take 1/3 tabular difference.

sin 21 13' = 0.36190

sin 21 12' = 0.36162

0.00028 difference

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 hypotenuse.

An acute angle and the opposite leg.

An acute angle and the adjacent leg.

The hypotenuse and a leg.

The two legs.