A pair of hikers sets off from their cabin and travels 2.62 km due North. After

Question

A pair of hikers sets off from their cabin and travels 2.62 km due North. After stopping for lunch, they travel 1.71 km in a direction 34.4° South of East. They then travel 0.836 km due East before stopping for a snack. Draw a diagram representing their travels and answer the following questions.

How far East of the cabin did the hikers travel before stopping for a snack?

How far North of the cabin did the hikers travel before stopping for a snack?

Their friends who stayed back at the cabin now wants to join them. What is the shortest distance they need to walk in order to get to the point where the original hikers are eating their snack?

Expressed as an angle North of East, what direction do the new hikers need to travel in order to get to the original hikers by traveling in a straight line? (Use 'deg' to represent units of degrees.)

Explanation / Answer

Path takenis shown in red

a)

Distance due east = bc + 0.836 km
=1.71 cos 34.4 + 0.836
= 2.247 km

b)
distance due North = 2.62 - 1b
=2.62 - 1.71 sin 34.4
= 1.654 km

c)
distance due North = 1.654 km
distance due east = 2.247 km

shortest distance= sqrt (1.654^2 + 2.247^2)
= 2.79 km

d)
angle = atan(distance due North / distance due east)
= atan (1.654/2.79)
= 30.7 degree

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.