**Problem Statement:**2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon.**Instruction:**A. Draw a diagram that models this scenario.**Explanation of Diagram:**1. **Initial Condition:** - **Building:** Represent the building as a vertical line of unknown height \( H \). - **Sun's Angle (60°):** Draw a horizontal line from the base of the building and a line tilted at a 60° angle above this horizontal line, representing the direction of the sunlight. - **Shadow:** Mark the point where this sunlight meets the ground. The horizontal distance from the base of the building to this point is the shadow length \( S \).2. **Later Condition:** - **Sun's Angle (30°):** Draw another horizontal line from the base of the building and another line tilted at a 30° angle above this horizontal line, representing the new direction of the sunlight. - **Extended Shadow:** Extend the shadow by 10 meters beyond the initial shadow length \( S \). Represent this total length as \( S + 10 \).3. **Geometric Relationships:** - Use trigonometric functions to relate the height of the building and the lengths of shadows. - For the initial shadow: \[ S = H \cdot \cot(60°) \] - For the later, longer shadow: \[ S + 10 = H \cdot \cot(30°) \]**Objective:** - Using the given angles and the increase in shadow length, compute the height of the building \( H \) and the lengths of the shadows \( S \) and \( S + 10 \) using trigonometric relationships.

Lets say initial length of the shadow was 'x' meter and height of the building is 'h' meter.

2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon. A. Draw a diagram that models this scenario

2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon. A. Draw a diagram that models this scenario

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem Statement:**
2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon.

**Instruction:**
A. Draw a diagram that models this scenario.

**Explanation of Diagram:**
1. **Initial Condition:**
- **Building:** Represent the building as a vertical line of unknown height \( H \).
- **Sun's Angle (60°):** Draw a horizontal line from the base of the building and a line tilted at a 60° angle above this horizontal line, representing the direction of the sunlight.
- **Shadow:** Mark the point where this sunlight meets the ground. The horizontal distance from the base of the building to this point is the shadow length \( S \).

2. **Later Condition:**
- **Sun's Angle (30°):** Draw another horizontal line from the base of the building and another line tilted at a 30° angle above this horizontal line, representing the new direction of the sunlight.
- **Extended Shadow:** Extend the shadow by 10 meters beyond the initial shadow length \( S \). Represent this total length as \( S + 10 \).

3. **Geometric Relationships:**
- Use trigonometric functions to relate the height of the building and the lengths of shadows.
- For the initial shadow:
\[ S = H \cdot \cot(60°) \]
- For the later, longer shadow:
\[ S + 10 = H \cdot \cot(30°) \]

**Objective:**
- Using the given angles and the increase in shadow length, compute the height of the building \( H \) and the lengths of the shadows \( S \) and \( S + 10 \) using trigonometric relationships.

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