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If θ is an acute angle, and its is given that 5 sinθ + 12 cosθ = 13, then what is the value of tanθ?

If θ is an acute angle, and its is given that 5 sinθ + 12 cosθ = 13, then what is the value of tanθ? Correct Answer 5/12

5 sinθ + 12 cosθ = 13

⇒ 5/13 sinθ + 12/13 cosθ = 1 (1)

We have, sin2θ + cos2θ = 1

Comparing it with equation (1)

sinθ = 5/13 and cosθ = 12/13

⇒ tanθ = sinθ/cosθ = (5/13)/(12/13) = 5/12

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