SOLUTION: A point A is 10.00 km due north of here. Another point B is 12.36 km from here on a line 17.4(degree) east of north. What is the distance from A to B? Can you include the diagram

Algebra ->  Trigonometry-basics -> SOLUTION: A point A is 10.00 km due north of here. Another point B is 12.36 km from here on a line 17.4(degree) east of north. What is the distance from A to B? Can you include the diagram       Log On


   

Question 903018: A point A is 10.00 km due north of here. Another point B is 12.36 km from here on a line 17.4(degree) east of north. What is the distance from A to B?
Can you include the diagram please. Thanks!
Please, I need help really bad..
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let North be positive y, let East be positive x.
You're at (0,0).
Draw a circle of radius 10.
Draw a circle of radius 12.36.
The first point is (0,10) since it only has a North (y) component.
To find the second point, build a right triangle starting at (0,0) with a hypotenuse that is 17.4 degrees from the y axis (East or positive x direction).
You can then calculate the leg lengths using the angle and the hypotenuse.
X leg : 12.36%2Asin%2817.4%29=3.69%7D%7D%0D%0AY+leg+%3A+%7B%7B%7B12.36%2Acos%2817.4%29=11.79
The second point is (3.69,11.79)

To calculate the distance between two points, use the distance formula,
D%5E2=%283.69-0%29%5E2%2B%2811.79-10%29%5E2
D%5E2=3.69%5E2%2B1.79%5E2
D%5E2=16.820
D=4.1km