In the figure below, BD bisects ∠ABC. What is the length of AB?
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Answer:
20.823 nautical miles
S20°E
Step-by-step explanation:
I assume you mean ° (degrees), not ' (minutes). There are 60 minutes in 1 degree.
S52°E means "south, 52° east", or 52° east of south.
S50°W means "south, 50° west", or 50° west of south.
1 knots = 1 nautical mile / hour, so the boat first travels 8 nautical miles from A to B, then 4.5 nautical miles from B to C, then finally back to A.
If we say A is at the origin, then the coordinates of B are:
(8 sin 52°, -8 cos 52°)
And the coordinates of C are:
(8 sin 52° − 4.5 sin 50°, -8 cos 52° − 4.5 cos 50°)
(2.857, -7.818)
So the distance from A to C is:
x = √(2.857² + (-7.818)²)
x ≈ 8.323
And the total distance of the race is:
d = 8 + 4.5 + 8.323
d = 20.823
The compass bearing from A to C is:
θ = atan(2.857 / 7.818)
θ ≈ S20°E
