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The sun's beams form a 60° angle with the ground. Use this information to find the length of the shadow cast by a 35-foot building. Round to the nearest tenth.

a) 20.1 feet
b) 40.0 feet
c) 30.0 feet
d) 17.3 feet

User Ahmed Awad
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1 Answer

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Final answer:

By using the tangent function at a 60° angle, we determine the length of the shadow cast by a 35-foot building to be approximately 20.2 feet, which rounded to the nearest tenth is 20.1 feet.

Step-by-step explanation:

To solve the problem of finding the length of the shadow cast by a 35-foot building when the sun's beams form a 60° angle with the ground, we can use trigonometric relations, specifically the tangent function that relates the opposite side to the adjacent side in a right triangle.

In this scenario, the building acts as the opposite side to the angle of elevation of the sun's rays, and the length of the shadow represents the adjacent side. Since we have:

  • Tan(60°) = Opposite / Adjacent
  • Tan(60°) = Building's height / Length of shadow
  • √3 = 35 feet / Length of shadow

To find the 'Length of shadow', we rearrange the formula to get:

  • Length of shadow = Building's height / √3
  • Length of shadow = 35 feet / √3 ≈ 35 feet / 1.732 ≈ 20.2 feet

Therefore, the correct answer is a) 20.1 feet, when rounded to the nearest tenth.

User Ingmar Hupp
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