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PSYCHO15rus [73]
3 years ago
11

If tan Θ=3/4, then evaluate 3sin Θ +2cos Θ

Mathematics
1 answer:
Alecsey [184]3 years ago
6 0

Answer:

3\sin\theta+2\cos\theta=\dfrac{17}{5}

Step-by-step explanation:

Given that,

The value of \tan\theta=\dfrac{3}{4}

We know that, \tan\theta=\dfrac{\text{perpendicular}}{\text{base}}

H^2=B^2+P^2

H is hypotenuse

H^2=3^2+4^2\\\\H=5

\sin\theta=\dfrac{P}{H}\\\\=\dfrac{3}{5}

And, \cos\theta=\dfrac{B}{H}=\dfrac{4}{5}

So,

3\sin\theta+2\cos\theta=3\times \dfrac{3}{5}+2\times \dfrac{4}{5}\\\\=\dfrac{9}{5}+\dfrac{8}{5}\\\\=\dfrac{17}{5}

So, the value is 17/5.

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