Create an equation using the definition of the sine of an angle.
≈ 53^(∘)
Practice makes perfect
Let's begin with recalling the definition of the sine of an angle.
If△ ABCis a right triangle with acute∠ A,
then the sine of∠ Ais the ratio of the length
of the leg opposite∠ Ato the length of
the hypotenuse.
Now let's look at the given picture. We are given that Ramon has a rolling backpack that is 3 34 feet tall when the handle is extended, and his hand is 3 feet from the ground. Let x represent the angle Ramon's backpack makes with the floor.
Next, we can write that the sine of x is the ratio of the length of the leg, 3, to the length of the hypotenuse, 3 34.
sin x=3/3 34
To find the value of x, we will rewrite the above equation using the inverse sine.
x=sin ^(-1)3/3 34
We can solve for x by evaluating the inverse sine using a calculator.
