A car leaves its garage and travels for 30km on a bearing of 145, then 10 km on a bearing of 250 Calculate a) the distance trave

Question

1 year ago

5

lled from the starting point b) the bearing of the starting point from the car.

1 answer:

OverLord2011 [107] · Answer 1 · 2023-10-06T07:41:27+03:00

The distance travelled from the starting point is 29 km , the bearing is 344 degree

The missing diagram is attached with the answer.

<h3>What is Bearing Angle ?</h3>

It is the horizontal angle between the object and another object.

It is given that the car starts from point travels for 30km on a bearing of 145, then 10 km on a bearing of 250

(a) the distance travelled from the starting point

It can be understood from the diagram that

To determine the distance , b is to determined4

By applying Cosine rule

b² = a² +c²-2ac cos $\rm \theta$

b² = 10² +30² - 2* 30*10 cos75

b² = 100+900 -600* 0.2588

b² = 100-155.2914

b² = 844.7

b = 29 km

Therefore the distance travelled from the starting point is 29 km.

(b) the bearing of the starting point from the car.

To determine the bearing ,

angle C has to be determined

By sine rule

sin C / c = sin B / b

sin C = sin 75 * 30 / 29

sin C = 0.9970

C = sin⁻¹ 0.9970

C = 85.59 degree

angle C = α +70 degree

α = 15.59 degree

Bearing = 70 + 20 + 9 0 + 90+74 = 244 degree

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