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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

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∘ 60^{\circ} relative to ground level. If an individual panel is 6767 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?\newlineChoose 11 answer:\newline(A) 33.53 33.5 \sqrt{3} in\mathrm{in} \newline(B) 33.52 33.5 \sqrt{2} in\mathrm{in} \newline(C) 33.5 33.5 in\mathrm{in} \newline(D) 13433 \frac{134 \sqrt{3}}{3} in\mathrm{in}

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Q. 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∘ 60^{\circ} relative to ground level. If an individual panel is 6767 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?\newlineChoose 11 answer:\newline(A) 33.53 33.5 \sqrt{3} in\mathrm{in} \newline(B) 33.52 33.5 \sqrt{2} in\mathrm{in} \newline(C) 33.5 33.5 in\mathrm{in} \newline(D) 13433 \frac{134 \sqrt{3}}{3} in\mathrm{in}
  1. Trigonometry Calculation: To find the height of the upper edge of the solar panel above the ground, we can use trigonometry. The length of the panel is the hypotenuse of a right-angled triangle, and the height above the ground is the side opposite the 60∘60^\circ angle. We can use the sine function to find this height.
  2. Sine Function Equation: The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. Therefore, we can write the equation: \newlinesin⁡(60∘)=height67 inches\sin(60^\circ) = \frac{\text{height}}{67 \text{ inches}}
  3. Substitute Values: We know that sin⁡(60∘)\sin(60^\circ) is equal to 32\frac{\sqrt{3}}{2}. \newlineSo, we can substitute this value into our equation: \newline32=height67 inches\frac{\sqrt{3}}{2} = \frac{\text{height}}{67 \text{ inches}}
  4. Solve for Height: Now, we solve for the height by multiplying both sides of the equation by 6767 inches: \newlineheight=67 inches×(32)\text{height} = 67 \text{ inches} \times (\frac{\sqrt{3}}{2})
  5. Final Height Calculation: After performing the multiplication, we get: \newlineheight=67×32\text{height} = \frac{67 \times \sqrt{3}}{2} inches \newlineheight=33.5×3\text{height} = 33.5 \times \sqrt{3} inches \newlineThe simplified expression for the height is 33.5333.5 \sqrt{3} inches, which corresponds to answer choice (A)(A).

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