Question

To the nearest hundredth, what is the sine of the acute angle formed by the line whose equation is y = 3x - 3 and the positive x-axis?

Answer 1

The sine of the acute angle is
`0.95`

Explanation:

using a graphing tool

see the attached figure

Let

A-----> the acute angle formed by the given line and the positive x-axis

In the right triangle XYZ

we know that

`sin(A)=(xy)/(xz)`

we have

`xy=3\ units`

`yz=1\ units`

Applying the Pythagoras Theorem find the value of xz

`xz^(2)=3^(2)+1^(2)\\ \\xz^(2)=10\\ \\xz=√(10)\ units`

substitute

`sin(A)=(3)/(√(10))=0.95`