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

Answer:

The sine of the acute angle is $0.95$

Step-by-step 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

$sin(A)=\frac{xy}{xz}$

we have

$xy=3\ units$

$yz=1\ units$

Applying the Pythagoras Theorem find the value of xz

$xz^{2}=3^{2}+1^{2}\\ \\xz^{2}=10\\ \\xz=\sqrt{10}\ units$

substitute

$sin(A)=\frac{3}{\sqrt{10}}=0.95$