Question

If tanθ=3677
, what is the value of sinθ
?

Answer 1

We are given

`\sf \tan( \theta) = (36)/(77)`

And we know that:

`\sf \tan( \theta) = (P )/(B)`

Thus, P = 36 and B = 77

Now by pythagoras theorem:

`{H} = \sqrt{ {P }^(2) + {B}^(2) }`

`{H} = \sqrt{ {36 }^(2) + {77}^(2) }`

`{H}= √( 1296 + 5929 )`

`{H} = √( 7225 )`

`{H} = 85`

Now, We know that;

`\sf \sin( \theta) = (P )/(H)`

`\sf \sin( \theta) = (36)/(85)`