Problem

144. Aviation From city \( A \) to city \( B \), a plane flies 650 miles at a bearing of \( 48^{\circ} \). From city \( B \) to city \( C \), the plane flies 810 miles at a bearing of \( 115^{\circ} \). Find the distance from city \( A \) to city \( C \) and the bearing from city \( A \) to city \( C \).

Solution

Step 1 :\( \alpha = 180^\circ - 48^\circ \)

Step 2 :\( \beta = 115^\circ - \alpha \)

Step 3 :Use Law of Cosines: \( AC = \sqrt{ 650^{2} + 810^{2} - 2 \times 650 \times 810 \times \cos{ \beta } } \)

Step 4 :Use Law of Sines: \( \sin \gamma = \frac{810 \sin \beta}{AC} \)

Step 5 :\( \gamma = \arcsin{(\sin \gamma)} \)

Step 6 :Bearing: \( B = \gamma + 48^\circ \)

From Solvely APP
Source: https://solvelyapp.com/problems/10780/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download