Math CentralQuandaries & Queries


Question from Tim:

How would I calculate the area in square feet of a "triangle" with sides:

Base is 36 feet; height is 70 feet; and the third side is an arch
(curve) of 77 feet.


Is the angle between the 36 foot side and the 70 foot side a right angle?


Tim wrote back

Yes it is, Harley.

Like the attached drawing. Thanks for the quick response!



I added some labels and a line to your diagram.

Tim's diagram

Triangle ABC is a right triangle so I can use Pythagoras Theorem to find the length of AB.

|AB|2 = |BC|2 + |CA|2
|AB|2 = 362 + 702
|AB|2 = 6196 so
|AB|= √6196 = 78.7 feet.

But this can't be. Certainly the arc from A to B is longer than the line segment from A to B. Can you check your measurements?



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