determine how far apart

Question

Two friends, Manpal and Jas, start from the same point but ride their bikes down two different paths. The paths meet at an angle of 28°. Manpal rides 25km down his path, while Jas rides 18km down his. Determine how far apart (to the nearest kilometere) the two are after their rides. Include a diagram with your solution. (4 marks)

Answer 1

use the law of cosines

It's a modified Pythagorean theorem for angles not 90 degrees

c^2 = a^2 + b^2 - 2ab(cosC)

c= distance between them. a= 18, b= 25 C=28

plug in the numbers solve for c. c= about 12.42 km

c^2= 18^2 + 25^2 - 2(18)(25)cos28

=324 + 625 - 900(.833) = 949 - 794.7 = 154.3

c = sqr154.7 = 12.42 km

c = 12 km