SOLUTION: Have no idea where to even begin to solve this problem. Any help is appreciated. The Grand Canyon Skywalk at Eagle Point is a horseshoe shaped steel frame with a glass floor loo

Algebra ->  Trigonometry-basics -> SOLUTION: Have no idea where to even begin to solve this problem. Any help is appreciated. The Grand Canyon Skywalk at Eagle Point is a horseshoe shaped steel frame with a glass floor loo      Log On


   

Question 1170350: Have no idea where to even begin to solve this problem. Any help is appreciated.
The Grand Canyon Skywalk at Eagle Point is a horseshoe shaped steel frame with a glass floor looking down to the Grand Canyon below. The Skywalk extends 70 feet over the canyon rim and is 10 feet wide. The walkway consists of a semicircle with a straight portion on each side
Path Width 10 feet 65 feet Outer Circle: 65 feet diameter Location of Light Tower .Inner Circle. 45 feet diameter 70 feet
A light tower is going to be installed on the left edge of the Skywalk .
The light will shine down to the opposite edge of the Skywalk
How tall does the light tower need to be if the angle of depression is 51°? (Round to 1 decimal place and be sure to include units.)
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break down this problem step-by-step.
**1. Understand the Geometry:**
* The Skywalk has a semicircular section and two straight sections.
* We're interested in the distance across the Skywalk where the light will shine.
* The light tower is on the left edge, and the light shines to the right edge.
* The angle of depression is given, and we need to find the height of the tower.
**2. Calculate the Total Width of the Skywalk:**
* The semicircle has an outer diameter of 65 feet.
* The straight portions are each 70 feet long.
* The total width from left to right is therefore the diameter of the semicircle.
* The width of the skywalk is 65 feet.
**3. Set Up the Trigonometry:**
* We have a right triangle formed by:
* The height of the light tower (opposite side).
* The width of the Skywalk (adjacent side).
* The line of sight of the light beam.
* The angle of depression is the angle between the horizontal and the line of sight. It's equal to the angle of elevation from the bottom of the triangle.
* We'll use the tangent function:
* tan(angle) = opposite / adjacent
**4. Solve for the Height:**
* tan(51°) = height / 65 feet
* height = 65 feet * tan(51°)
* tan(51°) ≈ 1.2349
* height ≈ 65 feet * 1.2349
* height ≈ 80.2685 feet
**5. Round to One Decimal Place:**
* The height of the light tower is approximately 80.3 feet.
**Final Answer:** The light tower needs to be approximately 80.3 feet tall.