I'll denote the identity function by . Then for any functions
with inverse
,
One important fact is that composition is associative, meaning for functions , we have
So given
we can compose the functions on either side with :
then apply the rules listed above:
Answer:
From Pine Knob: 56.57 km
From Colt Station: 20.71 km
Step-by-step explanation:
The triangle internal angle (P) at Pine Knob is 80°-65° = 15°.
The triangle internal angle (C) at Colt Station is 70° +65° = 135°.
The triangle internal angle (F) at the fire is 180° -15° -135° = 30°.
Then the law of sines tells us ...
(Pine Knob to Fire)/sin(C) = (Colt Station to Fire)/sin(P) = (40 km)/sin(F)
That is ...
Pine Knob to Fire = (40 km)·sin(C)/sin(F) = (40 km)·sin(135°)/sin(30°) ≈ 56.57 km
Colt Station to Fire = (40 km)·sin(15°)/sin(30°) ≈ 20.71 km
