Create an equation using the definition of the sine of an angle.
≈ 24 in.
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 the springboard Eric uses in his gymnastic class has 6-inch coils and forms an angle of 14.5^(∘) with the base. Let l represents the length of the springboard. We will assume that the coils are perpendicular to the base.
Next we can write that the sine of 14.5^(∘) is the ratio of the length of the opposite leg, 6, to the length of the hypotenuse, l.
sin 14.5^(∘)=6/l
We can solve for l by evaluating sin 14.5^(∘) using a calculator.
