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Steven is designing a handrail for a staircase and needs to determine what the length of the handrail will be. The top end of the handrail will be 8 feet above the bottom end of the handrail. The angle of depression from the top end of the handrail to the bottom end of the handrail will be 41.5^(@). Find the length, in feet, of the handrail. Round your answer to the nearest whole foot.

Steven is designing a handrail for a staircase and needs to determine what the length of the handrail will be. The top end of the handrail will be 88 feet above the bottom end of the handrail. The angle of depression from the top end of the handrail to the bottom end of the handrail will be 41.5∘41.5^{\circ}. Find the length, in feet, of the handrail. Round your answer to the nearest whole foot.

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Q. Steven is designing a handrail for a staircase and needs to determine what the length of the handrail will be. The top end of the handrail will be 88 feet above the bottom end of the handrail. The angle of depression from the top end of the handrail to the bottom end of the handrail will be 41.5∘41.5^{\circ}. Find the length, in feet, of the handrail. Round your answer to the nearest whole foot.
  1. Identify Triangle: Identify the right triangle formed by the height, length of the handrail, and the horizontal distance. Use the tangent function, which relates the angle of depression to the opposite side (height) and adjacent side (horizontal distance).
  2. Use Tangent Function: Rearrange the equation to solve for the horizontal distance.
  3. Rearrange Equation: Use the Pythagorean theorem to find the length of the handrail, which is the hypotenuse of the triangle.
  4. Use Pythagorean Theorem: Round the result to the nearest whole foot.

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