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8. In the figure, \( A, B \) and \( C \) are three points on a horizontal field. \( A \) is due west of \( B \), the bearing of \( B \) from \( C \) is \( 125^{\circ}, A B=430 \mathrm{~m} \) and \( B C=460 \mathrm{~m} \). (a) Find (i) the distance between \( A \) and \( C \), (ii) \( \angle A C B \), (iii) the bearing of \( C \) from \( A \), (iv) the area of \( \triangle A B C \). At a certain instant, a hot air balloon is at a point which is directly above \( C \). (b) Given that the angle of elevation of the hot air balloon from \( B \) is \( 5.2^{\circ} \), find the angle of elevation of the hot air balloon from \( A \).

          8. In the figure, \( A, B \) and \( C \) are three points on a horizontal field. \( A \) is due west of \( B \), the bearing of \( B \) from \( C \) is \( 125^{\circ}, A B=430 \mathrm{~m} \) and \( B C=460 \mathrm{~m} \).
(a) Find
(i) the distance between \( A \) and \( C \),
(ii) \( \angle A C B \),
(iii) the bearing of \( C \) from \( A \),
(iv) the area of \( \triangle A B C \).
At a certain instant, a hot air balloon is at a point which is directly above \( C \).
(b) Given that the angle of elevation of the hot air balloon from \( B \) is \( 5.2^{\circ} \), find the angle of elevation of the hot air balloon from \( A \).

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Added by Stephen C.

Precalculus: Functions and Graphs

Earl W. Swokowski, Jeffrey A. Cole 11th Edition

Chapter 7

Instant Answer

Solved by Expert Sheryl Ezze

04/26/2024

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We have a triangle \(ABC\) where \(A\) is due west of \(B\), the bearing of \(B\) from \(C\) is \(125^\circ\), \(AB = 430m\), and \(BC = 460m\). We need to find the distance between \(A\) and \(C\), the angle \(\angle ACB\), the bearing of \(C\) from \(A\), the Show more…

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8. In the figure, \( A, B \) and \( C \) are three points on a horizontal field. \( A \) is due west of \( B \), the bearing of \( B \) from \( C \) is \( 125^{\circ}, A B=430 \mathrm{~m} \) and \( B C=460 \mathrm{~m} \). (a) Find (i) the distance between \( A \) and \( C \), (ii) \( \angle A C B \), (iii) the bearing of \( C \) from \( A \), (iv) the area of \( \triangle A B C \). At a certain instant, a hot air balloon is at a point which is directly above \( C \). (b) Given that the angle of elevation of the hot air balloon from \( B \) is \( 5.2^{\circ} \), find the angle of elevation of the hot air balloon from \( A \).

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