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θ is acute and 3 sin θ + 4 cos θ = 5. Find tan θ.

Competition practiceTrigonometry

A3/4
B4/3
C3/5
D1

Step-by-Step Solution

(3 s in θ + 4 cos θ)^{2} + (4 s in θ - 3 cos θ)^{2} = 25

, so 4 sin θ − 3 cos θ = 0 and tan θ = 3/4. (Then sin θ = 3/5, cos θ = 4/5.)

Answer: A) 3/4

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