Bearing question

Question

A man observes a tree on a bearing of 68 degrees and a statue on a bearing of 150 degrees. The distance between the tree and the statue is 180m. Show all information on a sketch. Calculate the distances between

(a) The man and the tree. (b) the man and the statue

 

that's all the information for the question i got, am i missing a part?

Answer 1

A discussion of bearings is beyond the scope of this forum. The following site will help you understand the ideas.

http://precalculusnwr7.wikispaces.com/17.+Solve+bearing+and+orienteering+problems+with+law+of+sines+and+law+of+cosines.

 

Once you have made a diagram which represents the bearings, you will have a triangle, the hypotenuse of which will be 180m.

 

By subtracting 68^o from 90^o, you will get 22^o. Then, by subtracting 90^o from 150^o, you will get 60^o. The sum of 60^o and 22^o is 82^o, the angle of the triangle which will be opposite the side of 180m. You will then be able to figure the other two angles, which are 30^o and 68^o.

 

Let side a be the side opposite angle A = 30^o, and side b the side opposite angle B = 68^o.

You can than use the Sine Law to calculate the lengths of the two sides.

a/sin A = c/sin C

a/ sin 30^o = 180m/sin 82^o So a ≅ 89m

b/ sin B = c/sin C

b/sin 68^o = 180m/sin 82^o   So b ≅ 168m