The distance from port Q to the lighthouse L is 18.44 km
The bearing of port Q from the lighthouse L is 282.53°.
How do we find the distance and bearing?
Distance = Speed × Time
1.5hr × 12 m = 18km
The distance Aleena sails from port P to port Q is indeed 18 km when sailing for 1 and a half hours at an average speed of 12 km/h.
Aleena sails 18 km from port P to port Q.
port Q to the lighthouse L, → the scale given: 1 cm represents 4 km.
length on the diagram from P to Q
Length on diagram (in cm) = (actual length in km)/(Scale conversion factor (in km/cm))
18km/4 = 4.5
For the Pythagorean theorem:
c² = a² + b²
(QL) = √(Length LP)² +(Length PQ)²
(QL) = √(1² + 4.5² )
(QL) = √(1 + 20.25)
(QL) = 4.609
Actual distance (QL)=4.61 cm × 4 km/cm
Actual distance (QL) ≈ 18.44 km
tangent of the angle (θ) at lighthouse L:
tan(θ) = opposite/Adjacent = length PQ/Length LP
θ = arctan ( length PQ/Length LP)
Bearing of Q from L= 360° − θ
Given that we calculated Length PQ to be 4.5 cm and Length LP to be 1 cm, let's use these values to find the bearing.
The angle θ at lighthouse L, calculated using the correct lengths, is approximately 77.47°. This angle is measured from the east direction towards port Q.
To find the bearing of port Q from the lighthouse L, which is measured clockwise from north, we subtract this angle from 360°:
Bearing of Q from L=360°−θ
Bearing of Q from L=360°−77.47°
Bearing of Q from L = 282.53°