Question

Using trigonometric tables, find the approximate value of tan 72° 17'.

Answer 1

Given: Find tan 72° 17' using trigonometric tables.

Step-wise calculation:

1. From the tan tables for 72° values at 6' intervals we read:

tan 72° 12' = 3.1146

tan 72° 18' = 3.1334.

2. These two entries are 6' apart.

The difference in tan over 6' is 3.1334 – 3.1146 = 0.0188.

3. 72° 17' is 5' beyond 72° 12', i.e. `5/6` of the interval from 12' to 18'.

So interpolate linearly:

Increment = `5/6 xx 0.0188`

= 0.0156667

4. Add this to tan 72° 12':

tan 72° 17' ≈ 3.1146 + 0.0156667

tan 72° 17' = 3.1302667 ≈ 3.1303