Two cities are 2000 km apart and lie on the same north-south line. the latitude of the northernmost city is 52 Degrees N. what is the latitude of the other city? the radius of the earth is approx 6400km

(Do not round until the final answer. Then round to the nearest integer as needed)

We know that the angle θθ is related to the difference in latitudes between the two cities. Since the cities lie on the same north-south line, the angle θθ is the difference in latitude between the two cities.

Given that the difference in latitude between the cities is 52∘−ϕ252∘−ϕ2, we need to convert this to radians:

θ=52∘−ϕ2180∘⋅πθ=180∘52∘−ϕ2⋅π

We also know that d=2000d=2000 km and R=6400R=6400 km.

Therefore, we have:

2000=6400⋅52∘−ϕ2180∘⋅π2000=6400⋅180∘52∘−ϕ2⋅π

Now, we can solve for ϕ2ϕ2:

20006400⋅π=52∘−ϕ2180∘6400⋅π2000=180∘52∘−ϕ2

13.2⋅π=52∘−ϕ2180∘3.2⋅π1=180∘52∘−ϕ2

13.2⋅π=52−ϕ21803.2⋅π1=18052−ϕ2

To solve for ϕ2ϕ2, we can cross multiply:

180=(52−ϕ2)⋅(3.2⋅π)180=(52−ϕ2)⋅(3.2⋅π)

180=52⋅(3.2⋅π)−ϕ2⋅(3.2⋅π)180=52⋅(3.2⋅π)−ϕ2⋅(3.2⋅π)

ϕ2⋅(3.2⋅π)=52⋅(3.2⋅π)−180ϕ2⋅(3.2⋅π)=52⋅(3.2⋅π)−180

ϕ2=52⋅(3.2⋅π)−1803.2⋅πϕ2=3.2⋅π52⋅(3.2⋅π)−180

Now, we can calculate ϕ2ϕ2:

ϕ2=52⋅3.2⋅π−1803.2⋅πϕ2=3.2⋅π52⋅3.2⋅π−180

ϕ2=166.4π−1803.2πϕ2=3.2π166.4π−180

ϕ2=166.4π3.2π−1803.2πϕ2=3.2π166.4π−3.2π180

ϕ2=52−1803.2πϕ2=52−3.2π180

ϕ2≈52−18010.08ϕ2≈52−10.08180

ϕ2≈52−17.857ϕ2≈52−17.857

ϕ2≈34.143ϕ2≈34.143

Rounding to the nearest integer, the latitude of the other city is approximately 34∘34∘ N.

Two cities are 2000 km apart and lie on the same north-south line. the latitude of the northernmost city is 52 Degrees N. what is the latitude of the other city? the radius of the earth is approx 6400km (Do not round until the final answer. Then round to the nearest integer as needed)

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Two cities are 2000 km apart and lie on the same north-south line. the latitude of the northernmost city is 52 Degrees N. what is the latitude of the other city? the radius of the earth is approx 6400km

(Do not round until the final answer. Then round to the nearest integer as needed)