To calculate the projectile's range, we can use the equation for horizontal distance:
Range = (initial velocity * time of flight) * cos(angle)

To find the time of flight, we can use the equation for vertical displacement:
Vertical displacement = (initial vertical velocity * time) + (0.5 * acceleration due to gravity * time^2)

Given that the projectile is fired at an angle of 60 degrees:
Initial vertical velocity = initial velocity * sin(angle)
Initial vertical velocity = 80 m/s * sin(60) = 80 m/s * 0.866 = 69.28 m/s

Now, we can use the equation for vertical displacement:
100 m = (69.28 m/s * time) + (0.5 * 9.8 m/s^2 * time^2)

Simplifying the equation:
0.5 * 9.8 m/s^2 * time^2 + 69.28 m/s * time - 100 m = 0

Using the quadratic formula, we can find the time of flight:
time = (-b ± sqrt(b^2 - 4ac)) / (2a)
where a = 0.5 * 9.8 m/s^2, b = 69.28 m/s, and c = -100 m

time = (-69.28 m/s ± sqrt((69.28 m/s)^2 - 4 * 0.5 * 9.8 m/s^2 * -100 m)) / (2 * 0.5 * 9.8 m/s^2)

time ≈ 7.43 s (ignoring the negative value)

Now, we can calculate the range using the equation mentioned earlier:
Range = (80 m/s * 7.43 s) * cos(60)
Range ≈ 434.35 m

Therefore, the projectile's range is approximately 434.35 meters.

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