Please answer the question with diagram.

An aircraft flies 400km from a point O on a bearing of 25 degrees and then 700 km on a bearing of 80 degrees to arrive at B. How far north of O is B? How far east of O is B? Find the distance and bearing of B from O?

An aircraft flies 500 km on a bearing of 100 degrees and then 600 km on a bearing of 160 degrees. Find the distance and bearing of the finishing point from the starting point.

Please answer with a diagram.

Well, first, I would like to tell you that bearings are always written in three digits, excluding decimals. This is very important.

25 degrees is therefore written as 025 and 80 degrees is written as 080.

Have you drawn your diagram?

http://p1cture.me/images/60749931394088552691.png

Each time, use a right angle. I put the green dashed lines to help you. The elue dashed lines are what you have to look for in the first and second part and the red line is for the last part.

Give it a try, with the next number and post what you get! :)

Dear Unknown,

I am still at a loss. Kindly explain in detail with answers. I need it urgently for tomorrow.

I am highly obliged to be your student.

Regards,
Your student

1. Finding how far North of O is B.

a) We'll find how much A is north of O first.

Using the sketch, we know that the part of the vertical blue line is given by:

cos(25) = \frac{l}{400}

So,

l = 400cos(25) = 362.5 km

b) The last part is how far north B is to A.

Again, using trigonometry, we get:

cos(80) = \frac{H}{700}

H = 700cos(80) = 121.6 km

So, total distance North B is from O is 362.5 + 121.6 = 484 km

2. Finding how far East of O is B.

a) We'll find how much A is east of O first.

Using the sketch, we know that the part of the vertical blue line is given by:

sin(25) = \frac{w}{400}

So,

w = 400sin(25) = 169.0km

b) The last part is how far east B is to A.

Again, using trigonometry, we get:

sin(80) = \frac{F}{700}

F = 700sin(80) = 689.4 km

So, total distance North B is from O is 169.0 + 689.4 = 858 km

3. Now that you have both, use Pythagoras' Theorem to find the distance from O to B.

OB^2 = 484^2 + 858^2

OB^2 = 971202.8

OB =\sqrt{971202.8}

OB = 986 km

Thank you very much for your help. It is indeed valuable.