Question

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

Answer 1

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.