Create an equation using the definition of the sine of an angle.
≈ 1.2 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 David is building a bike ramp of the length of 3 12 feet long, and he wants the angle that the ramp makes with the ground to be 20^(∘). Let h represents the height of the ramp.
Next we can write that the sine of 20^(∘) is the ratio of the length of the leg, h, to the length of the hypotenuse, 3 12.
sin 20^(∘)=h/3 12
We can solve for h by evaluating sin 20^(∘) using a calculator.
