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 ).

Question

Accepted Answer

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 )

Answer

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 )

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 $C$ .

Answer

Popular Problems

144. Aviation From city A to city B, a plane flies 650 miles at a bearing of 48∘. From city B to city C, the plane flies 810 miles at a bearing of 115∘. Find the distance from city A to city C and the bearing from city A to city C.

Answer

Popular Problems

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 $C$ .