Question

Using tables, find the approximate value of θ, when tan θ = 4.62.

Answer 1

Given: tan θ = 4.62

Step-wise calculation:

1. From trigonometric tables nearest whole degrees:

Angle | tan θ 77° | 4.3315 78° | 4.7046

2. The value 4.62 lies between tan 77° and tan 78°.

Difference in tan across 1°

= 4.7046 – 4.3315

= 0.3731

Amount above tan 77°

= 4.62 – 4.3315

= 0.2885

Fraction of the degree

= `0.2885/0.3731`

= 0.7736

3. Convert fractional degree to minutes:

0.7736 × 60 ≈ 46.4′

So, θ ≈ 77° + 46.4′ ≈ 77°46.4′, rounded ≈ 77°47′.

θ ≈ 77°47′   ...(≈ 77.79°)