### Problem Description**Scenario:** A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 44° and that the angle of depression to the bottom of the tower is 26°. **Question:** How tall is the tower?**Input Box for Solution:** ```_____________ feet```### Solution ExplanationTo solve for the height of the tower, we can split the problem into two right triangle problems:1. Calculate the height from the window to the top of the tower using the angle of elevation.2. Calculate the height from the window to the base of the tower using the angle of depression.3. Sum these heights to find the total height of the tower.#### Detailed Steps:1. **Calculate the height from the window to the top of the tower:** - Tan(44°) = Opposite/Adjacent - Opposite (Height to the top) = 300 * Tan(44°)2. **Calculate the height from the window to the base of the tower:** - Tan(26°) = Opposite/Adjacent - Opposite (Height to the base) = 300 * Tan(26°)3. **Sum these heights:** - Total Height of the Tower = Height to the top of the tower + Height to the base of the towerBy inputting the respective trigonometric values into these formulas, the final height of the radio tower can be determined.

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Answered: A radio tower is located 300 feet from…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.2: Trigonometric Equations

Problem 22E

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### Problem Description

**Scenario:** A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 44° and that the angle of depression to the bottom of the tower is 26°.

**Question:** How tall is the tower?

**Input Box for Solution:**

```
_____________ feet
```

### Solution Explanation

To solve for the height of the tower, we can split the problem into two right triangle problems:

1. Calculate the height from the window to the top of the tower using the angle of elevation.
2. Calculate the height from the window to the base of the tower using the angle of depression.
3. Sum these heights to find the total height of the tower.

#### Detailed Steps:

1. **Calculate the height from the window to the top of the tower:**

- Tan(44°) = Opposite/Adjacent
- Opposite (Height to the top) = 300 * Tan(44°)

2. **Calculate the height from the window to the base of the tower:**

- Tan(26°) = Opposite/Adjacent
- Opposite (Height to the base) = 300 * Tan(26°)

3. **Sum these heights:**

- Total Height of the Tower = Height to the top of the tower + Height to the base of the tower

By inputting the respective trigonometric values into these formulas, the final height of the radio tower can be determined.

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A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 44° and that the angle of depression to the bottom of the tower is 26°. How tall is the tower? feet