Garret makes a ramp for his skateboard in the shape of a right triangle with a hypotenuse of 2ft, and a leg of 1f. He wants to use a trigonometric ratio to describe the relationship 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^(@)

Question

Garret makes a ramp for his skateboard in the shape of a right triangle with a hypotenuse of  2ft, and a leg of  1f. He wants to use a trigonometric ratio to describe the relationship 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^(@)

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Identify Triangle Angles: Garret has a right triangle with a hypotenuse of 2 feet and a leg of 1 foot. To find the trigonometric ratios, we need to identify the angles of the triangle. Since the hypotenuse is twice the length of one leg, this suggests that the triangle is a 30-60-90 triangle, where the angles are 30 degrees, 60 degrees, and 90 degrees. The side opposite the 30-degree angle is the shortest side, which is 1 foot in this case, and the hypotenuse is 2 feet. We can now evaluate the trigonometric expressions based on this information.Evaluate Sin 30^(@): For expression A, sin 30^(@), the sine of 30 degrees in a 30-60-90 triangle is the ratio of the opposite side to the hypotenuse, which is 1/2. Since Garret's ramp has these exact measurements, this expression can be used.Cannot Use Cos 45^(@): For expression B, cos 45^(@), the cosine of 45 degrees is the ratio of the adjacent side to the hypotenuse in a 45-45-90 triangle. However, Garret's ramp is not a 45-45-90 triangle, so this expression cannot be used.Evaluate Tan 30^(@): For expression C, tan 30^(@), the tangent of 30 degrees is the ratio of the opposite side to the adjacent side in a 30-60-90 triangle. Since we know the opposite side is 1 foot and the adjacent side (the other leg) would be √3 feet, the tangent of 30 degrees is 1/√3, which simplifies to √3/3. This expression can be used for Garret's ramp.Cannot Use Sin 45^(@): For expression D, sin 45^(@), the sine of 45 degrees is the ratio of the opposite side to the hypotenuse in a 45-45-90 triangle. Since Garret's ramp is not a 45-45-90 triangle, this expression cannot be used.Evaluate Cos 60^(@): For expression E, cos 60^(@), the cosine of 60 degrees is the ratio of the adjacent side to the hypotenuse in a 30-60-90 triangle. Since the adjacent side to the 60-degree angle is the shortest side, which is 1 foot, and the hypotenuse is 2 feet, the cosine of 60 degrees is 1/2. This expression can be used for Garret's ramp.Cannot Use Tan 45^(@): For expression F, tan 45^(@), the tangent of 45 degrees is the ratio of the opposite side to the adjacent side in a 45-45-90 triangle. Since Garret's ramp is not a 45-45-90 triangle, this expression cannot be used.

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