Answer:
Step-by-step explanation: determine how far the log traveled, we can use the Law of Cosines. This law allows us to find the length of one side of a triangle when we know the lengths of the other two sides and the included angle.
Given:
The first distance from the spotter to the log is a=45 feet.
The second distance from the spotter to the log is b=10 feet.
The angle between these two sightings is θ=60
∘
.
The Law of Cosines is given by:
c
2
=a
2
+b
2
−2abcos(θ)
where c is the distance the log traveled, which we need to find.
Plugging in the given values:
a=45 feet
b=10 feet
θ=60
∘
(which we convert to radians as cos function in most calculators and programming languages uses radians)
Let's compute c using this formula
