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A person walks in the following pattern: 3.0 km north, then 2.4 km west, and finally 5.0 km south. (a) How far and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

Respuesta :

Answer:

3.12 km

320.19°

Explanation:

From the diagram, the starting point is O.

The resultant is line OC.

Hence, using Pythagoras Theorem, we have that:

OC² = OE² + EC²

OC² = 2.4² + 2²

OC² = 5.76 + 4

OC² = 9.76

OC = 3.12 km

The angle, θ, will be:

tanθ = (2/2.4)

tanθ = 0.833

θ = 39.81°

Measuring counterclockwise from the East, the angle will be 360 - 39.81 = 320.19°.

Ver imagen Teebhabzie

Answer:

a) the distance is 3.12 km

b) Angle is 244.35 degrees

Explanation:

As per attached diagram, we construct a triangle OAB where:

OB = 2.4 km

AB = 2.0 km

OA = ??

Using Pythagoras theorem on triangle OAB to find OA:

[tex](OA)^{2} = (OB)^2 + (AB)^2\\(OA)^{2} = 2.4^2 + 2.0^2\\OA = 3.12 km[/tex]

The final angle will be equal to 180 (east to west) added to the angle AOB

[tex]Angle AOB = Tan^-^1 (\frac{5}{2.4})[/tex]

Angle AOB = 64.35 degrees

Adding AOB with the angle between east and west i.e. 180 degrees

Angle =  180 + Angle AOB

Angle = 244.35 degrees

Ver imagen babarzaib021