Hello, billionj!
Determine the length of the two longest sides on an isosceles triangle
with the angles of 36°, 72°, 72°, and the base length of 550 feet. This is probably not an acceptable solution to this problem.
But it is a fascinating bit of mathematical trivia . . . hope you enjoy it.
Code:
*
/ \
/36°\
/ \
/ \ φ
/ \
/ \
/ 72° 72° \
* - - - - - - - *
1
This is a very special isosceles triangle.
The ratio of the equal side to the base is: . . . . the Golden Ratio.
Hence, with this triangle:
Code:
*
/ \
/36°\
/ \
x / \
/ \
/ \
/ 72° 72° \
* - - - - - - - *
550
we have: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
The Fibonacci sequence: .
. . where each term is the sum of the preceding two terms.
The ratios of consecutive terms approach the Golden Mean.
. .
Hence, any pair of consecutive terms of the Fibonacci sequence
. . will form a triangle very close to the 36°-72°-72° triangle.
Example:
Code:
A
*
/ \
/ \
/ \
377 / \ 377
/ \
/ \
/ \
B * - - - - - - - * C
233
The vertex angle is: .
The base angles are: .