Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake
Answers
Given : On the path to the traveler's right, a sign reads "Mercer: 24 km."
On the path to the traveler's left, a sign reads "Turtle Lake: 17 km . Angle between path = 75 deg
To find : the distance between Mercer and Turtle Lake
Solution:
One is 24 km
Another is 17 kn
Angle between them are 75°
if this is considered a triangle 24 km * 17 km are two sides
Distance between Mercer and Turtle Lake will be third side
Using cosine formula of triangle
c² = a² + b² - 2abCosC
=> Distance² = 24² + 17² - 2(24)(17)Cos75
=> Distance² = 576 + 289 - 816(0.2588)
=> Distance² = 865 - 211.2
=> Distance² = 653.8
=> Distance = 25.57 km
the distance between Mercer and Turtle Lake = 25.57 km
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