Question #232655

A plane flies from Entebbe towards Kiko for 596 km on a bearing of 232 degrees. It then flies from Kikoto Daro for 880 km on a bearing of 258 degrees. It finally flies to Haraka for 458 km on a bearing of 346 degrees from Daro.

(a) How far north or south of Entebbe is /15mrks

(i) Kiko (ii) Haraka?

(b) How far west or east of Entebbe is Haraka?

(c) Calculate the bearing of Haraka from Entebbe


1
Expert's answer
2021-09-03T16:11:12-0400
E(0,0)E(0,0)

K(596sin(232°),596cos(232°))K(596\sin(232\degree), 596\cos(232\degree))

D(596sin(232°)+880sin(258°),D(596\sin(232\degree)+880\sin(258\degree),

596cos(232°)+880cos(258°))596\cos(232\degree)+880\cos(258\degree))

H(596sin(232°)+880sin(258°)+458sin(346°),H(596\sin(232\degree)+880\sin(258\degree)+458\sin(346\degree),

596cos(232°)+880cos(258°)+458cos(346°))596\cos(232\degree)+880\cos(258\degree)+458\cos(346\degree))



(a)

(i)

K(596sin(232°),596cos(232°))K(596\sin(232\degree), 596\cos(232\degree))


y=596cos(232°) km367 kmy=596\cos(232\degree)\ km\approx-367\ km

Kiko is 367 km south of Entebbe.


(ii)

H(596sin(232°)+880sin(258°)+458sin(346°),H(596\sin(232\degree)+880\sin(258\degree)+458\sin(346\degree),

596cos(232°)+880cos(258°)+458cos(346°))596\cos(232\degree)+880\cos(258\degree)+458\cos(346\degree))


y=596cos(232°)+880cos(258°)+458cos(346°)) kmy=596\cos(232\degree)+880\cos(258\degree)+458\cos(346\degree))\ km




105.5 km\approx-105.5\ km

Haraka is 105.5 km south of Entebbe.

(b)


H(596sin(232°)+880sin(258°)+458sin(346°),H(596\sin(232\degree)+880\sin(258\degree)+458\sin(346\degree),

596cos(232°)+880cos(258°)+458cos(346°))596\cos(232\degree)+880\cos(258\degree)+458\cos(346\degree))


x=596sin(232°)+880sin(258°)+458sin(346°)) kmx=596\sin(232\degree)+880\sin(258\degree)+458\sin(346\degree))\ km




1441.2 km\approx-1441.2\ km

Haraka is 1441.2 km west of Entebbe.


(c)


H(596sin(232°)+880sin(258°)+458sin(346°),H(596\sin(232\degree)+880\sin(258\degree)+458\sin(346\degree),

596cos(232°)+880cos(258°)+458cos(346°))596\cos(232\degree)+880\cos(258\degree)+458\cos(346\degree))


tanθ=yx\tan\theta=\dfrac{y}{x}

=596cos(232°)+880cos(258°)+458cos(346°)596sin(232°)+880sin(258°)+458sin(346°)=\dfrac{596\cos(232\degree)+880\cos(258\degree)+458\cos(346\degree)}{596\sin(232\degree)+880\sin(258\degree)+458\sin(346\degree)}

0.0732\approx0.0732

θ4.1867°\theta\approx4.1867\degree

bearing=360°90°θ265.8°bearing=360\degree-90\degree-\theta\approx265.8\degree

The bearing of Haraka from Entebbe is 265.8°.265.8\degree .



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