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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

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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.2: The Law Of Cosines
Problem 3E
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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.
Transcribed Image Text:### 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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