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The angles of elevation to an airplane from two points A and B on level ground are 54° and 72°, respectively. The points A and B are 2.3 miles apart, and the airplane is east of both points in the same vertical plane. (a) Draw a diagram that represents the problem. Show the known quantities on the diagram. 72° 54 54°

The angles of elevation to an airplane from two points A and B on level ground are 54° and 72°, respectively. The points A and B are 2.3 miles apart, and the airplane is east of both points in the same vertical plane. (a) Draw a diagram that represents the problem. Show the known quantities on the diagram. 72° 54 54°

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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# Law of Sines - Homework 3.1 ## Problem Statement The angles of elevation to an airplane from two points \( A \) and \( B \) on level ground are \( 54^\circ \) and \( 72^\circ \), respectively. The points \( A \) and \( B \) are 2.3 miles apart, and the airplane is east of both points in the same vertical plane. ### (a) Task Draw a diagram that represents the problem. Show the known quantities on the diagram. ## Diagram Explanation The diagram shows two right triangles formed by lines of sight from points \( A \) and \( B \) to the airplane: - **Angle at Point A**: \( 54^\circ \) - **Angle at Point B**: \( 72^\circ \) - **Distance between Points A and B**: 2.3 miles A vertical line illustrates the airplane's position vertically above the ground, creating two right angles with the lines of sight from \( A \) and \( B \). Each triangle's base is the ground distance between the point and the foot of the vertical line (airplane’s projection on the ground). These setups allow the use of trigonometry, specifically the Law of Sines, to calculate unknown distances.
Transcribed Image Text:# Law of Sines - Homework 3.1 ## Problem Statement The angles of elevation to an airplane from two points \( A \) and \( B \) on level ground are \( 54^\circ \) and \( 72^\circ \), respectively. The points \( A \) and \( B \) are 2.3 miles apart, and the airplane is east of both points in the same vertical plane. ### (a) Task Draw a diagram that represents the problem. Show the known quantities on the diagram. ## Diagram Explanation The diagram shows two right triangles formed by lines of sight from points \( A \) and \( B \) to the airplane: - **Angle at Point A**: \( 54^\circ \) - **Angle at Point B**: \( 72^\circ \) - **Distance between Points A and B**: 2.3 miles A vertical line illustrates the airplane's position vertically above the ground, creating two right angles with the lines of sight from \( A \) and \( B \). Each triangle's base is the ground distance between the point and the foot of the vertical line (airplane’s projection on the ground). These setups allow the use of trigonometry, specifically the Law of Sines, to calculate unknown distances.
## Homework 3.1 - Law of Sines **Tasks:** (b) Find the distance between the plane and point B. (Round your answer to two decimal places.) ________ mi (c) Find the altitude of the plane. (Round your answer to two decimal places.) ________ mi (d) Find the distance the plane must travel before it is directly above point A. (Round your answer to two decimal places.) ________ mi **Need Help?** - **Read It** - **Watch It** --- The section appears to be from a homework assignment on the Law of Sines, likely involving problems related to calculating distances and altitudes using trigonometric principles. Students are encouraged to use rounding for precision and provided with options for additional help through reading or watching resources.
Transcribed Image Text:## Homework 3.1 - Law of Sines **Tasks:** (b) Find the distance between the plane and point B. (Round your answer to two decimal places.) ________ mi (c) Find the altitude of the plane. (Round your answer to two decimal places.) ________ mi (d) Find the distance the plane must travel before it is directly above point A. (Round your answer to two decimal places.) ________ mi **Need Help?** - **Read It** - **Watch It** --- The section appears to be from a homework assignment on the Law of Sines, likely involving problems related to calculating distances and altitudes using trigonometric principles. Students are encouraged to use rounding for precision and provided with options for additional help through reading or watching resources.
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