Create an equation using the definition of the sine of an angle.
≈ 80 ft
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 angle of ascent of the first hill of a roller coaster is 55^(∘), and the length of the track from the beginning of the ascent to the highest point is 98 feet. Let h be the height of the roller coaster.
Next, we can write that the sine of 55^(∘) is the ratio of the length of the opposite leg, h, to the length of the hypotenuse, 98.
sin 55^(∘)=h/98
We can solve for h by evaluating sin 55^(∘) using a calculator.
