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 determine which trigonometric ratios can describe the relationship between the sides of Garret’s right triangle, we can use the definitions of sine, cosine, and tangent.
1. Sine (sin) of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse.
2. Cosine (cos) is the ratio of the length of the adjacent side to the hypotenuse.
3. Tangent (tan) is the ratio of the opposite side to the adjacent side.
In this scenario:
– The hypotenuse is 2 ft.
– One leg (which we can consider as opposite) is 1 ft.
The other leg (adjacent) can be calculated using the Pythagorean theorem:
[ c^2 = a^2 + b^2 ]
[ 2^2 = 1^2 + b^2 ]
[ 4 = 1 + b^2 ]
[ b^2 = 3 ]
[ b = sqrt{3} text{ ft} ]
Now, we need to identify the correct angles and their relationships:
– Angles corresponding to the sides would be derived from the triangle’s configuration (angles based on the opposite and adjacent sides).
Now let’s evaluate the options:
A. sin 30° = 1/2 – Not applicable.
B. cos 45° = 1/√2 – Not