Giovanni went to los angeles, california, for the summer to visit his cousins. he used a map of bus routes to get from the airport to his cousin's house. the distance from the airport to his cousin's house is 56km. on his map, the distance is 4 cm. what is the scale factor?

Step-by-step explanation:

You know that the actual distance from the airport to his cousin's house is 56 kilometers and on the map this distance is 4 centimeters.

Then, you need to make the conversion from kilometers to centimeters (Remember that ):

Therefore, you can apply this procedure in order to find the scale factor:

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

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step-by-step explanati∵∵∴∴on: