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

  • Thread starter Thread starter ketanco
  • Start date Start date
  • Tags Tags
    Angles Length
AI Thread Summary
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.
ketanco
Messages
15
Reaction score
0
Hello,
What is the value of x in the attached?
obviously angle EAD = EDA but then what?
the shape is irregular. View attachment 8599
 

Attachments

  • 06-4.jpg
    06-4.jpg
    25.9 KB · Views: 108
Mathematics news on Phys.org
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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top