MHB How Can the Sine Rule Help Determine Lengths in Irregular Shapes?

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The sine rule, or law of sines, can be applied to find unknown lengths in irregular shapes by relating the ratios of the lengths of sides to the sines of their opposite angles. In the given irregular shape, recognizing that angles EAD and EDA are equal is crucial for applying the sine rule effectively. By establishing the necessary relationships between the sides and angles, one can solve for the unknown length x. This method is particularly useful in complex geometries where traditional methods may not suffice. Utilizing the sine rule simplifies the process of determining lengths in irregular shapes.
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Hello,
What is the value of x in the attached?
obviously angle EAD = EDA but then what?
the shape is irregular. View attachment 8599
 

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ketanco said:
Hello,
What is the value of x in the attached?
obviously angle EAD = EDA but then what?
the shape is irregular.

How about using the sine rule, also known as the law of sines?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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