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lapo4ka [179]
1 year ago
10

Use the scale of 1cm=45 km

Mathematics
1 answer:
alex41 [277]1 year ago
3 0

Answer:

d = 7.4 cm is the distance between the two cities on the map.

Step-by-step explanation:

Let d = the distance measured on the map in centimeters (cm) between any two locations and let D be the actual distance in kilometers (km) between these same two locations.

Since the scale on the map is 1 cm = 45 km, then the ratio of the distance on the map to the actual distance is equal to 1cm/45 km; therefore the quotient of any measured distance d on the map divided by the corresponding much longer actual distance D would have to maintain (equal) this same ratio; In other words, we can set up the following proportion to solve for d given the actual distance D = 333 km as follows:

1 cm/45 km = d/D

Substituting, we get:

1 cm/45 km = d/333 km

d/333 km = 1 cm/45 km

(d/333 km)(333 km) = (1 cm/45 km)(333 km)

d = (333 km/45 km)(1 cm)

d = 7.4 cm is the distance between the two cities on the map.

Check:

1 cm/45 cm = d/333 km

1 cm/45 cm = 7.4 cm/333 km

1 cm/45 cm = 1 cm/45 km (Therefore, the distance ratio of the map has been maintained

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Step-by-step explanation:

step 1

Find the sin(\theta)

we have

csc(\theta)=\frac{3}{2}

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csc(\theta)=\frac{1}{sin(\theta)}

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step 2

Find the cos(\theta)

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sin^{2}(\theta) +cos^{2}(\theta)=1

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step 3

Find the tan(\theta)

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tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

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Simplify

tan(\theta)=-\frac{2\sqrt{5}}{5}

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