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?
 
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Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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