Questions: Find the direction of the resultant ant vector. θ=[?]° Round to the nearest hundredth.

Find the direction of the resultant ant vector. θ=[?]° Round to the nearest hundredth.
Transcript text: Find the direction of the resultant ant vector. \[ \theta=[?]^{\circ} \] Round to the nearest hundredth.
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Solution

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Solution Steps

Step 1: Find the components of vector v

The vector v is found by subtracting the initial point from the terminal point: (8-(-7), 15-5) = (15, 10)

Step 2: Find the direction of vector v

The direction angle θ of vector v = <x,y> is given by tan θ = y/x.

In this case, tan θ = 10/15 = 2/3. θ = arctan(2/3) ≈ 33.69°

Final Answer: The direction of the resultant vector is approximately 33.69°.

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