Question

Find the measure of angle θ in the following when θ is acute.

sin `(θ/3 + 10°) = 1/2`

Answer 1

Given:

Let x = `θ/3` + 10°

sin x = `1/2`

x = 30° or x = 150°   ... [within 0° − 180°, then restrict by 10° < x < 40° to pick 30°]

Since θ is acute, 0° < θ < 90° ⇒ 10° < x < 40°   ... [Since θ is acute, x hence choose 30°, not 150°.]

`θ/3 + 10°`

= `30° → θ/3 = 20°`

= θ = 60°