To solve the problem, let's address each part step by step:

Part a: Jari-jari lingkaran di garis lintang 45° LU

This asks for the radius of a circle at latitude 45° North (LU = Lintang Utara).

The formula to calculate the radius of the circle (or the effective radius of Earth) at a specific latitude $\phi$ is:

$r_{\text{circle}} = R \times \cos(\phi)$

where:

• $R$ is the radius of the Earth (given as 6,371 km),
• $\phi$ is the latitude (in this case, $\phi = 45^\circ$).

Now, let's calculate:

$r_{\text{circle}} = 6,371 \times \cos(45^\circ)$

We know that $\cos(45^\circ) = \frac{1}{\sqrt{2}} \approx 0.707$, so:

$r_{\text{circle}} = 6,371 \times 0.707 \approx 4,505.57 \, \text{km}$

So, the radius of the circle at 45° latitude is approximately 4,505.57 km.

Part b: Besar sudut dalam derajat di sepanjang garis bujur antara kedua kota

This part asks for the angle (in degrees) between the two cities along their longitude.

The formula to find the angle between two points on the same latitude given the distance between them is:

$\Delta \theta = \frac{d}{r_{\text{circle}}}$

where:

• $d$ is the distance between the two cities along the latitude (given as 1,500 km),
• $r_{\text{circle}}$ is the radius of the Earth at the given latitude (calculated as 4,505.57 km in part a).

Now, calculate the angle $\Delta \theta$:

$\Delta \theta = \frac{1,500}{4,505.57} \approx 0.333$

To convert this result to degrees, multiply by $180^\circ / \pi$:

$\Delta \theta_{\text{degrees}} = 0.333 \times \frac{180}{\pi} \approx 19.07^\circ$

So, the angle between the two cities along their longitude is approximately 19.07°.

Summary:

• a. The radius of the circle at 45° latitude is approximately 4,505.57 km.
• b. The angular distance between the two cities along the longitude is approximately 19.07°.

Do you want further details or have any questions?

Here are 5 additional questions to deepen your understanding:

1. What is the significance of the Earth's radius varying with latitude?
2. How would the calculation change if the cities were located closer to the equator?
3. Can you derive the same formula for the radius of the Earth at latitude using trigonometric principles?
4. What real-world applications rely on understanding distances between cities along a specific latitude?
5. How would you calculate the distance between two cities along a meridian (longitude) instead of a parallel?

Tip: When working with angles and distances on the Earth's surface, always check if you need to convert between radians and degrees depending on the formula you're using.