Finding the angle between a wall and a broken rope

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SUMMARY

The discussion centers on calculating the angle α between a wall and a broken rope using trigonometric functions. The user identifies the formation of a trapezium and seeks clarity on deriving the solution through the sine function. The key insight involves extending the right segment of the rope to meet the wall, establishing a right triangle where the hypotenuse is the entire length of the rope. This geometric approach allows for the application of trigonometric principles to find the angle α definitively.

PREREQUISITES
  • Understanding of basic trigonometric functions, specifically sine and cosine.
  • Familiarity with right triangle properties and the Pythagorean theorem.
  • Knowledge of geometric shapes, particularly trapeziums and triangles.
  • Ability to visualize geometric constructions and their relationships.
NEXT STEPS
  • Study the derivation of the sine function in right triangles.
  • Explore geometric constructions involving trapeziums and their properties.
  • Learn how to apply the Pythagorean theorem in real-world scenarios.
  • Investigate advanced trigonometric identities and their applications in geometry.
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Students and educators in mathematics, geometry enthusiasts, and anyone interested in applying trigonometric functions to solve practical problems involving angles and lengths.

bolzano95
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Homework Statement
The following problem is to find an angle α
Relevant Equations
α=?
I tried to work out the solution using h. I get a trapezium, but there is always a lack of additional information. I looked up the solution and BAM, there is this simple equation for sinα.
I really don't understand how do we get such a solution. I leaned you can use trigonometric functions in a right triangle, but here I really don't get it how to work out α.
sind:b.png
 
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Make a straight line continuing the right rope to the left until it hits the wall. This continuation has the same length as the left part of the rope. This line and the right part of the rope together therefore has the same length as the entire rope. Use trigonometry with this as the hypothenuse.
 
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