Answer to Question #236270 in Math for luka

Question #236270

A boat sails from port A to port B which is 50 km away on a bearing of 126 degrees from A. It then sails to C which is 46 km away on a bearing of 170degrees from B. The boat continues to sail on a course of 045degrees from C to D for 65 km.

(a) How far south of A is D? (4marks)

(b) How far east of A is D? (4marks)

(c) Calculate the bearing of D from A. (3marks)

(first draw the figure indicating the given data.) (4marks)


1
Expert's answer
2021-09-21T04:59:39-0400

A(0,0)A(0,0)


B(50cos(36°),50sin(36°))B(50\cos(36\degree), -50\sin(36\degree))


C(50cos(36°)+46cos(80°),C(50\cos(36\degree)+46\cos(80\degree),

50sin(36°)46sin(80°))-50\sin(36\degree)-46\sin(80\degree))


D(50cos(36°)+46cos(80°)+65cos(45°),D(50\cos(36\degree)+46\cos(80\degree)+65\cos(45\degree),

50sin(36°)46sin(80°)+65sin(45°))-50\sin(36\degree)-46\sin(80\degree)+65\sin(45\degree))


(a)


50cos(36°)+46cos(80°)+65cos(45°)050\cos(36\degree)+46\cos(80\degree)+65\cos(45\degree)-0


=50sin(36°)+46sin(80°)65sin(45°)=50\sin(36\degree)+46\sin(80\degree)-65\sin(45\degree)

28.728(km)\approx28.728(km)

(b)


0(50sin(36°)46sin(80°)+65sin(45°))0-(-50\sin(36\degree)-46\sin(80\degree)+65\sin(45\degree))


=50cos(36°)+46cos(80°)+65cos(45°)=50\cos(36\degree)+46\cos(80\degree)+65\cos(45\degree)

94.401(km)\approx94.401(km)

(c)


θ=180°tan1(xDyD)\theta=180\degree-\tan^{-1}(\dfrac{|x_D|}{|y_D|})

=180°tan1(50cos(36°)+46cos(80°)+65cos(45°)50sin(36°)+46sin(80°)65sin(45°))=180\degree-\tan^{-1}(\dfrac{50\cos(36\degree)+46\cos(80\degree)+65\cos(45\degree)}{50\sin(36\degree)+46\sin(80\degree)-65\sin(45\degree)})

106.9°\approx106.9\degree

The bearing of D from A is 106.9°.106.9\degree.


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