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How far would you have to be from the base of the object to get an angle of elevation of 20 degrees?  Draw a diagram and show work.  Round to the nearest foot.  My eye level is 5.67 feet.

How far would you have to be from the base of the object to get an angle of elevation of 20 degrees?  Draw a diagram and show work.  Round to the nearest foot.  My eye level is 5.67 feet.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.1: Law Of Sines
Problem 1ECP: For the triangle shown, A=30, B=45, and a=32 centimeters. Find the remaining angle and sides.
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How far would you have to be from the base of the object to get an angle of elevation of 20 degrees?  Draw a diagram and show work.  Round to the nearest foot.  My eye level is 5.67 feet.

 

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Angle of elevation not depression

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These are suppose to be for angle of elevation, not depression.  The base of the object is on the ground.  I am on the ground.  My eye level is 5.67 from the ground.  I  looking up.

**Topic: Calculating the Angle of Elevation** When you stand 52 feet from the base of an object, the angle of elevation to the top of the object can be determined by using the height difference and distance from the object. Follow these steps to solve a similar problem: ### Question: If you stood 52 feet from the base of the object, what would be the angle of elevation to the top of the object (as measured from your eye level)? #### Note: 1. Remember to subtract your eye level of 5.67 feet to find the triangle’s height. 2. Round to the nearest degree. 3. Draw a diagram and show your work. ### Diagram Explanation: - **Person Height:** 5.67 feet - **Distance to Object (Base):** 52 feet - **Adjusted Height of Object:** The total height of the object minus the height of the person's eye level. ### Step-by-Step Solution: 1. **Unknown Height Calculation (Adjusted for Eye Level):** \[ \text{Total height of object} = 52 \text{ feet} \] \[ \text{Height above eye level} = 52 \text{ feet} - 5.67 \text{ feet} = 21.13 \text{ feet} \] 2. **Using Trigonometric Function (Tangent) to Determine the Angle:** \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] \[ \tan(\theta) = \frac{21.13 \text{ feet}}{52 \text{ feet}} \] 3. **Calculate the Angle:** \[ \theta = \tan^{-1}\left(\frac{21.13}{52}\right) \] 4. **Final Answer:** \[ \theta \approx 22^\circ \] **Note:** - Make sure to use a calculator set to degree mode to get the angle in degrees. ### Answer: **22 degrees** ### Diagram Representation: On the diagram: - The person is drawn at 5.67 feet tall. - The horizontal distance from the person to the object’s base is 52 feet. - The height of the object is indicated as "unknown." - The calculation shows \(21.13\) feet as
Transcribed Image Text:**Topic: Calculating the Angle of Elevation** When you stand 52 feet from the base of an object, the angle of elevation to the top of the object can be determined by using the height difference and distance from the object. Follow these steps to solve a similar problem: ### Question: If you stood 52 feet from the base of the object, what would be the angle of elevation to the top of the object (as measured from your eye level)? #### Note: 1. Remember to subtract your eye level of 5.67 feet to find the triangle’s height. 2. Round to the nearest degree. 3. Draw a diagram and show your work. ### Diagram Explanation: - **Person Height:** 5.67 feet - **Distance to Object (Base):** 52 feet - **Adjusted Height of Object:** The total height of the object minus the height of the person's eye level. ### Step-by-Step Solution: 1. **Unknown Height Calculation (Adjusted for Eye Level):** \[ \text{Total height of object} = 52 \text{ feet} \] \[ \text{Height above eye level} = 52 \text{ feet} - 5.67 \text{ feet} = 21.13 \text{ feet} \] 2. **Using Trigonometric Function (Tangent) to Determine the Angle:** \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] \[ \tan(\theta) = \frac{21.13 \text{ feet}}{52 \text{ feet}} \] 3. **Calculate the Angle:** \[ \theta = \tan^{-1}\left(\frac{21.13}{52}\right) \] 4. **Final Answer:** \[ \theta \approx 22^\circ \] **Note:** - Make sure to use a calculator set to degree mode to get the angle in degrees. ### Answer: **22 degrees** ### Diagram Representation: On the diagram: - The person is drawn at 5.67 feet tall. - The horizontal distance from the person to the object’s base is 52 feet. - The height of the object is indicated as "unknown." - The calculation shows \(21.13\) feet as
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