Tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ?

[TristanH]

tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2) ?

Folks,

In the solution guide to Kline's calculus book, he gives the following in working a problem:

tan(t) = x/a => sin(t) = x/sqrt( a^2 + x^2)

Can someone explain why this is the case?

Thanks,

Tristan

 

[rock.freak667]

tan(t)=Opposite/Adjacent. Draw a right-angled triangle with the side opposite to the angle ,t, as x and the adjacent side to it as a. Then use pythagoras' theorem.

 

[TristanH]

I just figured this out on my own. For anyone who is curious:

tan(t) = x/a means the opposite and adjacent legs of a right triangle with angle t, are x and a respectively. By the Pythagorean Therom, this implies that the hypotenuse is sqrt(a^2 + x^2). Since sin t = opp/hyp, sin t = x/sqrt( a^2 + x^2). QED

 

[Gib Z]

tan(t)=Opposite/Adjacent. Draw a right-angled triangle with the side opposite to the angle ,t, as x and the adjacent side to it as a. Then use pythagoras' theorem.

I just figured this out on my own. For anyone who is curious:

tan(t) = x/a means the opposite and adjacent legs of a right triangle with angle t, are x and a respectively. By the Pythagorean Therom, this implies that the hypotenuse is sqrt(a^2 + x^2). Since sin t = opp/hyp, sin t = x/sqrt( a^2 + x^2). QED

lol ?