Question

Look at the figure:

An image of a right triangle is shown with an angle labeled x.

If tan x° = 11 divided by r and cos x° = r divided by s, what is the value of sin x°?

sin x° = s divided by 11
sin x° = 11 divided by s
sin x° = 11r
sin x° = 11s

Answer 1

sin x° = 11 divided by s

Explanation:

Given,

tan x° = 11 divided by r

`\implies tan x^(\circ)=(11)/(r)`

Also, cos x° = r divided by s

`\implies cos x^(\circ)=(r)/(s)`

We know that,

`(sinx^(\circ))/(cos x^(\circ))=tan x^(\circ)`

`\implies sinx^(\circ)= tan x^(\circ)* cos x^(\circ)` ( by cross multiplication )

By substituting the values,

`sin x^(\circ)=(11)/(r)* (r)/(s)=(11r)/(rs)=(11)/(s)`

⇒ sin x° = 11 divided by s

Answer 2

sin(x°) = 11/s

Explanation:

The tangent is the ratio of sine to cosine, so ...

tan(x°) = sin(x°)/cos(x°)

Multiplying by cos(x°) gives ...

sin(x°) = cos(x°)·tan(x°) = (r/s)·(11/r)

sin(x°) = 11/s