Question

Using tables, find the approximate value of θ, when cos θ = 0.6879.

Answer 1

Given: cos θ = 0.6879 (θ acute)

Step-wise calculation:

1. From cosine values or a cosine table we find

cos 46° ≈ 0.69466

cos 47° ≈ 0.68200

Hence, 46° < θ < 47°.

2. Difference across 1°:

0.69466 – 0.68200 

= 0.01266

3. Difference from cos 46° down to given value:

0.69466 – 0.68790

= 0.00676

4. Fraction of the degree

= `0.00676/0.01266` 

= 0.534

5. Convert fraction to minutes:

0.534 × 60 ≈ 32.04′ ≈ 32′.

θ ≈ 46° 32′.