A circular reception tent has a center pole 30 feet high, and the poles along the outside are 9 feet high. Assume that the distance from the outside poles to the center pole is 25 feet. (Round your answ two decimal places.) (a) What is the slope of the line that follows the roof of the reception tent? ft/ft (b) How high is the tent 8 feet in from the outside poles? ft
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Problem Description
A circular reception tent has a center pole 30 feet high, and the poles along the outside are 9 feet high. Assume the distance from the outside poles to the center pole is 25 feet. (Round your answers to two decimal places.)
#### Questions:
(a) **What is the slope of the line that follows the roof of the reception tent?**
\[ \_ \_ \_ \_ \_ \_ \] ft/ft
(b) **How high is the tent 8 feet in from the outside poles?**
\[ \_ \_ \_ \_ \_ \_ \] ft
(c) **Ropes are used to stabilize the tent following the line of the roof of the tent to the ground. How far away from the outside poles are the ropes attached to the ground?**
\[ \_ \_ \_ \_ \_ \_ \] ft
### Explanation
This problem involves calculating the slope of the roof line, the height of the tent at a certain point, and the distance for rope stabilization. Each question requires applying geometric and algebraic concepts to determine the answers.
1. **Slope Calculation**: Determine the angle of inclination from the outside to the center pole.
2. **Height Calculation**: Use the slope to find the height at a specific point inward from the perimeter.
3. **Rope Distance**: Calculate how far the stabilizing ropes reach based on the slope.
The problem applies concepts of linearity and right triangle trigonometry to analyze real-world applications in tent construction and stability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74894f78-ccb5-452f-bebb-59c8a1f546c3%2F914169fb-9903-4ef2-9ae3-3002eb786456%2Fpr5fuvq_processed.png&w=3840&q=75)
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