What is the largest equilateral triangle that can be inscribed in a regular pentagon with side length 1?

Question

eyust707 · Answer

my intuition says it will look something like this:
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eyust707 · Answer

theres probably an easier way but the only thing i can think of is to create a system of equations that that must satisfy

anonymous · Answer

could you walk me through it?

eyust707 · Answer

i honestly dont know how exactly... but i could exaplin to you my thought process

eyust707 · Answer

what level math is this for?

anonymous · Answer

haha really high level

eyust707 · Answer

yea its not an easy problem

eyust707 · Answer

lets start with the angles

eyust707 · Answer

each one is 72 degrees

anonymous · Answer

anonymous · Answer

This is no where near high level mathematics! Hint: http://www.drking.org.uk/hexagons/misc/deriv1.html (This is for hexagon)

eyust707 · Answer

that doesnt actually prove thats the biggest one but if we assume so its just simple trig

anonymous · Answer

how did you know that the other angle is 72?

eyust707 · Answer

360/5

dumbcow · Answer

no it would be 540/5

sum interior = 180(n-2)

eyust707 · Answer

ahh yes 72 is the central angles

eyust707 · Answer

clearly its bed time for me

dumbcow · Answer

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now use law of sines
$$x = \frac{\sin 108}{\sin 48}$$