Question 1170350
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.