Kendra F. answered • 06/11/17

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Since the race finishes at the starting location the net displacement vector will be zero.

A + B + C + D = 0

Solve for the components of vector D taking up and right as positive.

**Horizontal component (right is positive, left is negative)**

3.40cos(40) - 5.10cos(35) - 5.30cos(23) + Dcos(θ) = 0

-6.45 + Dcos(θ) = 0

Dcos(θ) = 6.45 km

**Vertical Component (up is positive, down is negative)**

3.40sin(40) + 5.10sin(35) - 5.30sin(23) - Dsin(θ) = 0

3.04 - Dsin(θ) = 0

3.04 km = Dsin(θ)

Trig Identity

tan(θ) = sin(θ)/cos(θ)

tan(θ) = 3.04/6.45

arctan(3.04/6.45) = θ

25.24° = θ

Plug in the angle

Dcos(25.24) = 6.45 km

D = 6.45/cos(25.24)

D = 7.13 km