A farmer plans to install solar collection panels to provide winter heating for the livestock. The most efficient panel angle for winter heating in the farm's region is 60^(@) relative to ground level. If an individual panel is 67 inches (in) long and installed on the ground according to these instructions, what is the height, in in, of the upper edge above the ground? Choose 1 answer: (A) 33.5sqrt3 in (B) 33.5sqrt2 in (C) 33.5in (D) (134sqrt3)/(3) in

Question

A farmer plans to install solar collection panels to provide winter heating for the livestock. The most efficient panel angle for winter heating in the farm's region is  60^(@) relative to ground level. If an individual panel is 67 inches (in) long and installed on the ground according to these instructions, what is the height, in in, of the upper edge above the ground? Choose 1 answer: (A)  33.5sqrt3 in (B)  33.5sqrt2 in (C)  33.5in (D)  (134sqrt3)/(3) in

Bytelearn · Accepted Answer

Identify Triangle Components: The problem involves a right triangle where the solar panel forms the hypotenuse, the height above the ground is the opposite side, and the angle with the ground is 60 degrees. We can use the sine function to find the height because sine relates the opposite side to the hypotenuse in a right triangle.Apply Sine Function: Using the sine function: sin(60 degrees) = height / hypotenuse. We know the hypotenuse is 67 inches, so we can solve for the height: height = sin(60 degrees) * 67 inches.Calculate Height: The sine of 60 degrees is equal to sqrt(3)/2. Therefore, height = (sqrt(3)/2) * 67 inches.Perform Multiplication: Now we perform the multiplication: height = (sqrt(3)/2) * 67 = (67sqrt(3))/2 inches.Simplify Expression: Simplify the expression: height = (67sqrt(3))/2 inches. This simplifies to 33.5sqrt(3) inches, which matches one of the answer choices.

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