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Law of Cosines: When there is no right angle
Law of Cosines: When there is no right angle
How does the Law of Cosines extend our ability to calculate distances and angles in a two-joint robot arm?
Learning Intentions:
Apply c² = a² + b² − 2ab·cos(C) to find the gap distance or joint angle in a non-right triangle formed by a two-joint robot arm.
Apply c² = a² + b² − 2ab·cos(C) to find the gap distance or joint angle in a non-right triangle formed by a two-joint robot arm.
Today's Concept:
A two-joint robot arm forms a triangle. Almost none of those triangles have a right angle. When there's no right angle, SOHCAHTOA breaks — it requires one. You need a different tool.
The Law of Cosines works for any triangle: c² = a² + b² − 2ab·cos(C). Today you measure a real gap distance with string, then calculate it with the formula. The two values should match within about 1 cm. The formula isn't abstract — it's describing the same physical triangle you can hold in your hands.
SOHCAHTOA
Right Triangle
Law of Cosines
SSS
SAS
The Ambiguous Case of SSA
Types of Triangles
Station 1
Station 1
Explore It - Law of Cosines
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