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B 150m 86° 120m G

B 150m 86° 120m G

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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A hot air balloon is fixed to the ground at point F and G by two ropes.  If FBG is 86°, how far apart are points F and G?

This educational diagram depicts a trigonometric problem involving a hot air balloon (B) and two distinct observation points (F and G) on the ground. ### Description and Explanation: - **Hot Air Balloon (B):** The balloon is shown in the air, with a point B representing the balloon's position. - **Observation Points (F and G):** These two points are situated on the ground on a straight horizontal line. - **Distance Measurements:** - The distance between point F and the point directly below the balloon is 150 meters. - The distance between point G and the point directly below the balloon is 120 meters. - **Angle of Elevation:** - The angle of elevation from point F to the hot air balloon is given as 86°. This is the angle formed between the ground and the line of sight from point F to the balloon at point B. ### Educational Concepts: This diagram is useful for understanding several concepts in trigonometry and geometry: 1. **Angle of Elevation:** The angle above the horizontal line from the observer's eye to some point above their head. 2. **Trigonometric Functions in Real-Life Situations:** Students can apply trigonometric functions (sine, cosine, tangent) to calculate heights or distances that aren't directly measurable. 3. **Right Triangle Properties:** By identifying the right triangle formed by the vertical height of the balloon, the distance on the ground, and the line of sight, students can use fundamental trigonometric identities to solve for unknown lengths or angles. ### Application: Students can be prompted to calculate the height of the hot air balloon using the right triangle properties and given measurements. They would need to use the tangent function, where tan(86°) = height / 150m, to find the height of the balloon from point F. Similarly, they could use the given distances and angle to verify the vertical height from point G or apply the Pythagorean theorem if needed. Overall, the diagram provides a practical example of applying mathematical concepts to a tangible situation.
Transcribed Image Text:This educational diagram depicts a trigonometric problem involving a hot air balloon (B) and two distinct observation points (F and G) on the ground. ### Description and Explanation: - **Hot Air Balloon (B):** The balloon is shown in the air, with a point B representing the balloon's position. - **Observation Points (F and G):** These two points are situated on the ground on a straight horizontal line. - **Distance Measurements:** - The distance between point F and the point directly below the balloon is 150 meters. - The distance between point G and the point directly below the balloon is 120 meters. - **Angle of Elevation:** - The angle of elevation from point F to the hot air balloon is given as 86°. This is the angle formed between the ground and the line of sight from point F to the balloon at point B. ### Educational Concepts: This diagram is useful for understanding several concepts in trigonometry and geometry: 1. **Angle of Elevation:** The angle above the horizontal line from the observer's eye to some point above their head. 2. **Trigonometric Functions in Real-Life Situations:** Students can apply trigonometric functions (sine, cosine, tangent) to calculate heights or distances that aren't directly measurable. 3. **Right Triangle Properties:** By identifying the right triangle formed by the vertical height of the balloon, the distance on the ground, and the line of sight, students can use fundamental trigonometric identities to solve for unknown lengths or angles. ### Application: Students can be prompted to calculate the height of the hot air balloon using the right triangle properties and given measurements. They would need to use the tangent function, where tan(86°) = height / 150m, to find the height of the balloon from point F. Similarly, they could use the given distances and angle to verify the vertical height from point G or apply the Pythagorean theorem if needed. Overall, the diagram provides a practical example of applying mathematical concepts to a tangible situation.
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