Find the latitude soup of me equator sum that when one travels along the latitude for 80 nm, a change of 2° in longitude is made.

Habari Pretty! Ninaona umefanya kazi nzuri kwenye maswali haya. Wacha tuangalie majibu yako.

5) Tafuta umbali katika nautical miles kati ya pointi A($45^\circ N, 35^\circ W$) na B($45^\circ N, 100^\circ E$) kando ya sambamba ya latitudo.

Kazi yako ni sahihi kabisa.
Tofauti ya longitudo ni $35^\circ + 100^\circ = 135^\circ$.
Umbali katika km:

$$D_{km} = \frac{135^\circ}{360^\circ} \times 2\pi (6370 \text{ km}) \cos(45^\circ) \approx 10609.95 \text{ km}$$

Umbali katika nm:

$$D_{nm} = \frac{10609.95 \text{ km}}{1.852 \text{ km/nm}} \approx 5728.97 \text{ nm}$$

Kukamilisha kwa namba nzima:

$$\boxed{\text{5729 nm}}$$

✅ Correct. Mahesabu yako yanalandana na jibu sahihi.

6) Tafuta latitudo kusini mwa ikweta ambapo unaposafiri kando ya latitudo kwa 80 nm, mabadiliko ya $2^\circ$ katika longitudo hufanywa.

Umeandika fomula sahihi:

$$D = \frac{\theta}{360^\circ} \times 2\pi R \cos \alpha$$

Kutoka hapa, unahitaji kupanga upya fomula ili kupata $\cos \alpha$ na kisha $\alpha$.
Umbali $D = 80 \text{ nm} = 148.16 \text{ km}$. Tofauti ya longitudo $\theta = 2^\circ$.

$$\cos \alpha = \frac{D \times 360^\circ}{2\pi R \theta}$$ $$\cos \alpha = \frac{148.16 \text{ km} \times 360^\circ}{2\pi (6370 \text{ km}) \times 2^\circ} \approx 0.66631$$ $$\alpha = \cos^{-1}(0.66631) \approx 48.21^\circ$$

Kwa kuwa inatafutwa latitudo kusini mwa ikweta:

$$\boxed{48.21^\circ S}$$

✅ Correct. Fomula yako ni sahihi na jibu la mwisho ni $48.21^\circ S$.

7) Tafuta umbali kati ya pointi P($35^\circ N, 50^\circ E$) na Q($26^\circ 30' S, 50^\circ E$) kwenye uso wa Dunia.

Kazi yako ni sahihi. Pointi ziko kwenye longitudo moja, kwa hivyo tunatumia fomula ya duara kuu.
Tofauti ya latitudo ni $35^\circ + 26^\circ 30' = 61.5^\circ$.
Umbali katika km:

$$D_{km} = \frac{61.5^\circ}{360^\circ} \times 2\pi (6370 \text{ km}) \approx 6824.96 \text{ km}$$

Kukamilisha kwa namba nzima:

$$\boxed{\text{6825 km}}$$

Umbali katika nm:

$$D_{nm} = \frac{6824.96 \text{ km}}{1.852 \text{ km/nm}} \approx 3685.18 \text{ nm}$$

Kukamilisha kwa namba nzima:

$$\boxed{\text{3685 nm}}$$

✅ Correct. Mahesabu yako yanalandana na majibu sahihi.