Jake left the campsite hiking in the direction N52oW at the

Jake left the campsite hiking in the direction N52^oW at the constant rate of 4.2 miles per hour. At the same time, Sara left the campsite hiking in the direction S58^oW at 3.5 miles per hour. Two hours later, how far apart are Jake and Sara?

Question 1 options:

3.0 miles

4.5 miles

8.9 miles

12.6 miles

Solution

jake travelling in N52^oW at 4.2 miles per hours

distance covered in 2 hours = 4.2 * 2 = 8.4 miles

sara travelling in S58^oW at 3.5 miles per hour

distance covered in 2 hours = 3.5*2 = 7 miles

angle between jake and sara = (90 - 52) + (90 - 58) = 38 + 32 = 70 degrees

hence applying law of cosines to find the unknown side

c^2 = a^2 + b^2 - 2ab cos C

c^2 = 8.4^2 + 7^2 - 2*8.4*7 cos 70

c^2 = 79.338

c = 8.9 miles

after 2 hours jake and sara are 8.9 miles apart