Question

Using tables, find the approximate value of θ, when sin θ = 0.4878.

Answer 1

Given: sin θ = 0.4878

Step-wise calculation:

1. Locate nearest tabulated sines from trig tables:

sin 29°11' ≈ 0.4876

sin 29°12' ≈ 0.4879

2. Interpolate between 29°11' and 29°12':

Difference between table sines

= 0.4879 – 0.4876

= 0.0003

Difference from the lower entry

= 0.4878 – 0.4876

= 0.0002

Fraction of `1′ = 0.0002/0.0003` 

= `2/3 ≈ 0.6667′`

3. Add this to 29°11′:

θ = 29°11′ + 0.6667′

= 29°11.6667′ ≈ 29°11′40″   ...(≈ 29.1933°)

Hence, using tables θ ≈ 29°11.6′ approximately 29°11′40″.