Question

It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the
lighthouse is N31°E. How far has the ship sailed from the port? Round your answer to the nearest 0.1 km
O A. 3.5 km
O B. 3.1 km
O C. 3.7 km​

Answer 1

Answer:

correct option is  C. 3.7 km

Step-by-step explanation:

given data

A to Port B = 4.7 km

lighthouse = N73°E

lighthouse = N31°E

solution

we get here first  $\angle$ B and  

here

$\angle$ A = 90 - 73 = 17°

$\angle$ B =  73 - 31 = 42°

and

sum of all angle 180° so

$\angle$ A +  

17° + 42° +  $\angle$ C = 180°  

solve it we get

$\angle$ C = 121°

Now we use here sin law that is

$\frac{b}{sinB} = \frac{c}{sinC}$   ........................2

put here value and we get

$\frac{b}{sin42} = \frac{4.7}{sin121}$  

solve it we get

b = 3,7 km

so correct option is  C. 3.7 km