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.
A. sin 30°
B. cos 45°
C. tan 30°
D. sin 45°
E. cos 60°
F. tan 45°
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.
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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°)