Simplify, using trigonometric tables

tan 45° 27’ + sin 20°

First we consider tan 45° 27’.

We write tan 45° 27’ = tan 45° 24’ + 3’.

The relevant part of the tangent table is given below.

From the table, we have

tan 45° 24’ = 1.0141

Mean difference for 3’ = 0.0018

We know that mean difference is to be added in the case of tangent.

∴ tan 45° 27’ = 1.0141 + 0.0018 = 1.0159

Then, consider sin 20°,

The relevant part of the sine table is given below.

From the table, we have

Sin 20° = 0.3420

∴ tan 45° 27’ + sin 20° = 1.0159 + 0.3240 = 1.3399