Garret makes a ramp for his skateboard in the shape of a right triangle with a hypotenuse of 2 ft, and a leg of 1 ft. He wants to use a trigonometric ratio to describe the relationship between these two sides. Select all of the expressions that he could use.

To solve this problem, we need to identify the appropriate trigonometric ratios that relate to the given sides of the right triangle.

In a right triangle, we can define the following trigonometric ratios based on the opposite side (O), adjacent side (A), and hypotenuse (H):

– Sine (sin): (sin(theta) = frac{text{Opposite}}{text{Hypotenuse}})

– Cosine (cos): (cos(theta) = frac{text{Adjacent}}{text{Hypotenuse}})

– Tangent (tan): (tan(theta) = frac{text{Opposite}}{text{Adjacent}})

In Garret’s triangle:

– Hypotenuse (H) = 2 ft

– One leg (Adjacent A) = 1 ft

To find the opposite leg (O), we can use the Pythagorean theorem: (H^2 = O^2 + A^2).

Thus, (2^2 = O^2 + 1^2) leads to:

[4 = O^2 + 1 Rightarrow O^2 = 3 Rightarrow O = sqrt{3} , text{ft}.]

Now let’s analyze the given options based on known angles and sides.

1. A. sin 30°: (sin(30°)