Question

Nen,

Problem: Two towns, A and B, located along the coast of the Pacific Ocean are 30
km apart on a north-south line. From a ship, the line of sight of town A is W30°N,
while that of town B is S400W.
1. How far is the ship from town A?
2. How far is the ship from town B?
​

Answer 1

Explanation:

From the picture attached,

m∠COB = 90° - m∠BOS

= 90° - 40°

= 50°

tan(30°) =
`(AC)/(OC)`

`(1)/(√(3))=(AC)/(OC)`

AC =
`(OC)/(√(3))` ------(1)

Similarly, tan(50°) =
`(BC)/(OC)`

BC = OC[tan(50°)] -------(2)

Now AC + BC = 30 cm

By substituting the values of AC and BC from equation (1) and (2),

`(OC)/(√(3))+OC(\text{tan}50)=30`

(1.769)OC = 30

OC = 16.96

1). cos(30°) =
`(OC)/(AO)`

`(√(3))/(2)= (16.96)/(OA)`

`OA=19.58` cm

Therefore, distance between the ship and town A is 19.58 cm.

2). cos(50°) =
`(OC)/(OB)`

0.6428 =
`(16.96)/(OB)`

OB = 26.38 cm

Therefore, distance between the ship and town B is 26.38 cm.