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
[tex]\frac{PR}{sin R}[/tex] = [tex]\frac{PQ}{sin Q}[/tex]
[tex]\frac{10.5}{sin 77.5°}[/tex] = [tex]\frac{PQ}{sin 59.7°}[/tex]
PQ = ([tex]\frac{10.5}{Sin 77.5°}[/tex])(sin 59.7°)
= 9.29
