Question

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

Answer 1

`3\sin\theta+2\cos\theta=(17)/(5)`

Explanation:

Given that,

The value of
`\tan\theta=(3)/(4)`

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

`H^2=B^2+P^2`

H is hypotenuse

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

`\sin\theta=(P)/(H)\\\\=(3)/(5)`

And,
`\cos\theta=(B)/(H)=(4)/(5)`

So,

`3\sin\theta+2\cos\theta=3* (3)/(5)+2* (4)/(5)\\\\=(9)/(5)+(8)/(5)\\\\=(17)/(5)`

So, the value is 17/5.