A signal tower forms an elevation such that tan θ = 3/4. Compute sin 2θ.
Show answer & explanation
Correct answer: A
Explanation
Given:
tanθ = 3 / 4
By the formula:
sin2θ = 2tanθ / (1 + tan²θ)
sin2θ = 2 × (3/4) / (1 + (3/4)²)
= (6/4) / (1 + 9/16)
= (6/4) / (25/16)
= (6/4) × (16/25)
= 96 / 100
= 24 / 25