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Building 68 120 ft Note: Figure is not drawn to scale. 68° is the 120 ft. is the and the height of the building is the: So, use to solve for the height of the building. The building is: feet tall (to the nearest whole foot).

Building 68 120 ft Note: Figure is not drawn to scale. 68° is the 120 ft. is the and the height of the building is the: So, use to solve for the height of the building. The building is: feet tall (to the nearest whole foot).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Solving for the Height of a Building Using Trigonometry #### Problem Statement: We are given a situation where we need to find the height of a building. The given data includes an angle of elevation and the distance from the observer to the base of the building. #### Diagram: The diagram provided shows a right-angled triangle where: - One angle is 68°. - The adjacent side (ground distance from the observer to the base of the building) is 120 feet. **Note:** The figure is not drawn to scale. #### Step-by-Step Solution: 1. Identify the given parts: - 68° is the **angle of elevation**. - 120 ft. is the length of the **adjacent side** (the distance from the observer to the building). 2. Identify what needs to be found: - The goal is to find the height of the building, which corresponds to the **opposite side** of the right triangle. 3. Use the tangent function for solving for the height: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \] Where: - \(\theta\) is the angle of elevation (68°), - The adjacent side is 120 feet. 4. Insert the values into the tangent function: \[ \tan(68°) = \frac{\text{height of the building}}{120 \text{ ft}} \] 5. Solve for the height of the building: \[ \text{Height of the building} = \tan(68°) \times 120 \text{ ft} \] 6. Calculating the value: \[ \text{Height of the building} \approx 2.475 \times 120 \text{ ft} \approx 297 \text{ ft} \] Therefore, the building is approximately **297 feet** tall (to the nearest whole foot). #### Using the Interactive Functionality: Students can use the provided buttons for sin, cos, tan, angle of elevation, hypotenuse, opposite side, adjacent side, to input and calculate the solution as follows: - Select "**tan**" for the trigonometric function. - Choose "angle of elevation" and set it to 68°. - Set the "adjacent side" to 120 ft. - Calculate
Transcribed Image Text:### Solving for the Height of a Building Using Trigonometry #### Problem Statement: We are given a situation where we need to find the height of a building. The given data includes an angle of elevation and the distance from the observer to the base of the building. #### Diagram: The diagram provided shows a right-angled triangle where: - One angle is 68°. - The adjacent side (ground distance from the observer to the base of the building) is 120 feet. **Note:** The figure is not drawn to scale. #### Step-by-Step Solution: 1. Identify the given parts: - 68° is the **angle of elevation**. - 120 ft. is the length of the **adjacent side** (the distance from the observer to the building). 2. Identify what needs to be found: - The goal is to find the height of the building, which corresponds to the **opposite side** of the right triangle. 3. Use the tangent function for solving for the height: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \] Where: - \(\theta\) is the angle of elevation (68°), - The adjacent side is 120 feet. 4. Insert the values into the tangent function: \[ \tan(68°) = \frac{\text{height of the building}}{120 \text{ ft}} \] 5. Solve for the height of the building: \[ \text{Height of the building} = \tan(68°) \times 120 \text{ ft} \] 6. Calculating the value: \[ \text{Height of the building} \approx 2.475 \times 120 \text{ ft} \approx 297 \text{ ft} \] Therefore, the building is approximately **297 feet** tall (to the nearest whole foot). #### Using the Interactive Functionality: Students can use the provided buttons for sin, cos, tan, angle of elevation, hypotenuse, opposite side, adjacent side, to input and calculate the solution as follows: - Select "**tan**" for the trigonometric function. - Choose "angle of elevation" and set it to 68°. - Set the "adjacent side" to 120 ft. - Calculate
### Solving for the Height of a Building Using Trigonometry In this lesson, we will solve for the height of a building using trigonometry. We are given a right triangle where the angle adjacent to the base is 68° and the length of the base (opposite to the right angle) is 120 feet. #### Diagram Explanation The diagram shows a right triangle with: - An angle measuring 68° - A base (adjacent side to the 68° angle) of 120 feet - The height of the building is the side opposite to the 68° angle The diagram is annotated with text stating, "Note: Figure is not drawn to scale." #### Problem Statement Fill in the blanks to solve for the height of the building. \[ 68^\circ \text{ is the } \_\_\_\_\_ \text{and the height of the building is the } \_\_\_\_\_. \text{So, use } \_\_\_\_\_ \text{ to solve for the height of the building. The building is } \_\_\_\_\_ \text{ feet tall (to the nearest whole foot).} \] #### Step-by-Step Solution 1. Identify the trigonometric function to use: Since we are given the length of the adjacent side (base) and we need to find the opposite side (height), we will use the tangent function. \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] 2. Substitute the given values into the tangent function: \[ \tan(68^\circ) = \frac{\text{height}}{120 \text{ ft}} \] 3. Solve for the height: \[ \text{height} = 120 \text{ ft} \times \tan(68^\circ) \] Using a calculator: \[ \tan(68^\circ) \approx 2.475 \] Therefore: \[ \text{height} \approx 120 \text{ ft} \times 2.475 \approx 297 \text{ ft} \] 4. Round the height to the nearest whole foot: \[ \text{height} = 297 \text{ ft} \] So, the building is approximately 297 feet tall. ### Answer 68°
Transcribed Image Text:### Solving for the Height of a Building Using Trigonometry In this lesson, we will solve for the height of a building using trigonometry. We are given a right triangle where the angle adjacent to the base is 68° and the length of the base (opposite to the right angle) is 120 feet. #### Diagram Explanation The diagram shows a right triangle with: - An angle measuring 68° - A base (adjacent side to the 68° angle) of 120 feet - The height of the building is the side opposite to the 68° angle The diagram is annotated with text stating, "Note: Figure is not drawn to scale." #### Problem Statement Fill in the blanks to solve for the height of the building. \[ 68^\circ \text{ is the } \_\_\_\_\_ \text{and the height of the building is the } \_\_\_\_\_. \text{So, use } \_\_\_\_\_ \text{ to solve for the height of the building. The building is } \_\_\_\_\_ \text{ feet tall (to the nearest whole foot).} \] #### Step-by-Step Solution 1. Identify the trigonometric function to use: Since we are given the length of the adjacent side (base) and we need to find the opposite side (height), we will use the tangent function. \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] 2. Substitute the given values into the tangent function: \[ \tan(68^\circ) = \frac{\text{height}}{120 \text{ ft}} \] 3. Solve for the height: \[ \text{height} = 120 \text{ ft} \times \tan(68^\circ) \] Using a calculator: \[ \tan(68^\circ) \approx 2.475 \] Therefore: \[ \text{height} \approx 120 \text{ ft} \times 2.475 \approx 297 \text{ ft} \] 4. Round the height to the nearest whole foot: \[ \text{height} = 297 \text{ ft} \] So, the building is approximately 297 feet tall. ### Answer 68°
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