Question

A farmer is designing a field for his new horse. In order for the field to fit into his farm, the angle θ must be less than 40◦, calculate the size of the angle, with a suitable level of accuracy, and justify if the field will fit or not.

Answer 1

The field will not fit

Explanation:

To find the angle, we will use cosine rule;

c² = (a² + b² - 2abcosC)

C in this case is θ

Thus;

15² = (8² + 20² - 2(8 × 20)cos θ)

225 = (64 + 400 - 320cos θ)

464 - 225 = 320cos θ

cos θ = 239/320

θ = cos^(-1) 0.7469

θ = 41.68°

Thus angle is not less than 40° as recommended. Thus, the field will not fit.