Question

A boat leaves the harbor entrance and travels 27 miles in the direction ??? ° ?. The captain then travels for another 16 miles in the direction ??? ° ?, which is the boat’s final position. How far is the harbor entrance from the boat’s final position? What is the bearing of the boat from the harbor entrance? Round your answers to the nearest WHOLE numbers.

Answer 1

a) N39 E b) S52 E

we have to find blue line distance.

angles on opposite side of transversal are always equal.

using Laws of Cosines:

'a' and 'b' are length of two sides and 'C' is angle between them.

'c' is third side of triangle

here we have

a=27

b=16

C=52+39=91

so

c=31.62

Distance between harbor entrance and final point is 32.

Bearing of boat from harbor entrance.

The bearing of a point is the number of degrees in the angle measured in a clockwise direction from the north line .

again using law of cosines

angle between two lines is 'C' , WHICH we have to find and these two lines are a=32 , b=27

here we also have third line c=16

C=30 degree

Bearing will be 39+30=69 degree