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: .