Question

During an orienteering hike, two hikers start at point A and head in a direction 30 degrees west of south to point B. They hike 6 miles from point A to point B. From point B, they hike to point C and then from point C back to point A, which is 8 miles directly north of point C. How many miles did they hike from point B to point C?

Answer 1

ok... so draw a diagram



use the law of cosines to find the distance BC

\[BC^2 = AB^2 + AC^2 - 2 \times AB \times AC \times \cos(A)\]

substitute your values and evaluate

Answer 2

@campbell_st is it 13.6?

Answer 3

you need to take the square root of 16.8616

for the correct answer