Question

Two lighthouses are located 20 miles from one another on a north-south line. If a boat is spotted S 25o E from the northern lighthouse and N 35o E from the southern lighthouse, how much closer is the closest lighthouse to the boat than the lighthouse furthest away?
The northern lighthouse is 7.2 miles closer than the southern lighthouse.


The southern lighthouse is 9.8 miles closer than the northern lighthouse.


The southern lighthouse is 3.4 miles closer than the northern lighthouse.


The southern lighthouse is 23 miles closer than the northern lighthouse.

Answer 1

Answer:

The southern lighthouse is 3.4 miles closer than the northern lighthouse

Step-by-step explanation:

From the figure we see that we need to find the distances AK and BK.

The measure of the third angle K is = 180- 25-35= 120 degrees

Using the sine ratios we can find the two distances

From the figure

The northern distance is given by

20/ sin 120 = kA/ sine 35

KA= 20 sine 35/ sine 120

KA= 13.25 miles

The southern distance is given by

20 /sine 120= KB / sine 25

20 sine 25/ sine 120 = KB

KB= 9.759=9.76 miles

Difference between the two miles =

13.25 miles - 9.76 miles = 3.49 miles

The southern lighthouse is 3.4 miles closer than the northern lighthouse

Option C is correct