Question

A ship is sailing due north. At a certain point the bearing of a lighthouse is N 42.8∘E and the distance is 10.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.7∘E. How far did the ship travel between the two observations of the lighthouse?

Answer 1

Answer:

How far did the ship travel between the two observations of the lighthouse  = 9.29

Step-by-step explanation:

the first step to answer this question is drawing the illustration as the attachment.

P is the ship, R is the light house and Q is the bearing.

PR is the distance between the ship and the light house, PR = 10.5

∠P = 42.8°, ∠Q = 59.7°

Thus, ∠R = 180° - ∠P  - ∠Q

               = 180° - 42.8°- 59.7°

               = 77.5°

PQ is the the distance of the ship moving. We can use the sinus equation

$\frac{PR}{sin R}$ = $\frac{PQ}{sin Q}$

$\frac{10.5}{sin 77.5°}$ = $\frac{PQ}{sin 59.7°}$

PQ = ($\frac{10.5}{Sin 77.5°}$)(sin 59.7°)

     = 9.29