SOLUTION: A man travels 5 km due north from his starting point and then travels a further 8 km in a straight line in the direction 30 degrees east of north.How far is he from his starting po

Question 1089471: A man travels 5 km due north from his starting point and then travels a further 8 km in a straight line in the direction 30 degrees east of north.How far is he from his starting position ?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you could solve this by creating right triangles, or you can solve using the following formula:

b^2 = a^2 + c^2 - 2 * a * c * cos(B)

this, i believe, is called the law of cosines.

here's a reference:

http://www.mathwarehouse.com/trigonometry/law-of-cosines-formula-examples.php

here's a picture of my worksheet.

$$$

the triangle is labeled ABC.

A is the starting point.
B is the point 5 km due north.
C is the point 8 km due 30 degrees east of north.

angle B in the triangle is 150 degrees, since it is supplementary to the 30 degree angle.

side a is opposite angle A of the triangle.
side b is opposite angle B of the triangle.
sice c is opposite angle C of the triangle.

this fits the law of cosines since you are looking for the side opposite the known angle and you have the measure of the side adjacent to that angle.

the worksheet has the details of the calculations.

cos(150) is equal to -.8660254038

the rest is just solving the equation.

any questions, give me a shout.

otherwise, i believe you have all that you need.

another law that is sometimes useful is the law of sines.

a reference to that can be found here:

http://www.mathwarehouse.com/trigonometry/law-of-sines/formula-and-practice-problems.php

RELATED QUESTIONS
could you please help me to find the answer in this question. a boat travels 3 km due... (answered by student141910)

A person travels 12 km due north;then 15 km due east;after that 15 km due west and then... (answered by macston)

a man travels 7 km due north and than travels 3 km due east and than travels 3 km due... (answered by amoresroy)

A man drives 12 km to the north and then 15 km to the east. What are the magnitude and... (answered by josgarithmetic)

A man drives 12 km to the north and then 15 km to the east. What are the magnitude and... (answered by ikleyn)

a ship travels 6 km due South, 5 km due East and then 4 km due South. How far is it from... (answered by Alan3354)

A person travels 12 km due North, then 15 km due East, after that 15 km due West and then (answered by Cromlix)

A person travels 2 km due North, then 15 km due East, after that 19 km due West and then... (answered by addingup)

A person travels 2 km due North, then 15 km due East, after that 19 km due West and then... (answered by math_helper)