Problem 2 of 3

Rubie leaves home and walks north for 4.8 km, then west for 3.6 km and arrives at school.

(a) Sketch a vector diagram of this situation.

(b) What is the shortest distance between Rubie's home and school?

(c) What direction must she take to follow this path home?

(d) Design another route for Rubie to return home from school assuming she starts off in the direction S20°W. Sketch any route she could take and indicate all distances and directions.

**Solution**

A)

B) a² + b² = c²

4.8 Km² + 3.6 Km² = C²

SQRROOT: 36 =6 Km

The shortest distance between rubies home and school is 6 Km.

C) SohCahToa

TanO/A

Tan 3.6/4.8

Tan-¹ 3.6/4.8

=36.87° West of South

In order for Rubie to get home , she would have to move at 36.87° West of South for 6 Km.

D)In order for Rubie to get home, she would first move to S 20°W for 2.4 Km's.

I now have Side-Angle Side, as shown in diagram D

I would now use the Cosine Law

The Cosine Law is:

c² = a² +b² - 2ab Cos(C)

Plugging in the Equation:

6²+2.4²- 2(2.4)(6)Cos(20°)

= 14.7

SqrRoot(14.7) = 3.83 Km

After Heading in her initial direction of S 20°W for 2.4 km, she would turn, and move at an as of yet undefined vector for 4.665 Km.

In order to find the angles, we would employ the Sine Law

The Sine Law is as follows:

(sin(A)/a) = (Sin(B)/b) = (Sin(C)/c)

Plugging in the Equation:

Sin(20°)/3.83 = Sin(B)/4.8

(Sin(20)/3.83)(4.8) = Sin(B)

.4286414 = Sin(B)

Sin~¹(.4286414) = B

B = 25.381°

In order to get home, she would have to walk 2.4 Km at S20°W, then turn towards S 45.381° W

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