While attending the circus, you see an amazing site. theodore the fantastic frog. theodore sits on a stand with his mouth 5 feet 6 inches above the ground. people walk past theodore one-by-one. when standing directly in front of the frog, each person is exactly one foot from theodore. the amazing part occurs when a person passes in front of theodore. he sticks his tongue out and touches their nose. if the tallest person's nose that theodore can touch has a nose that is exactly 6 feet 4 inches off the ground, answer the following questions. a. what would be the height of the nose of the shortest person that theodore could lick? b. what is the maximum distance that theodore can stick his tongue out?

Theodore sits on a stand with his mouth 5 feet 6 inches above the ground:
x1=0
y1=5 feet 6 inches=(5 feet)(12 inches / 1 foot) 6 inches=60 inches 6 inches
y1=66 inches
(x1, y1)=(0, 66)

When standing directly in front of the frog, each person is exactly one foot from Theodore:
x2=1 foot→x2=12 inches

If the tallest person's nose that Theodore can touch has a nose that is exactly 6 feet 4 inches off the ground:
y2=6 feet 4 inches=(6 feet)(12 inches / 1 foot) 4 inches=72 inches 4 inches
y2=76 inches
(x2, y2)=(12, 76)

a. What would be the height of the nose of the shortest person that Theodore could lick?
y3=?
y3=y1-dy
dy=y2-y1=76 inches-66 inches→dy=10 inches
y3=y1-dy=66 inches-10 inches=56 inches=48 inches + 8 inches
y3= (48 inches) ( 1 foot / 12 inches) 8 inches
y3=4 feet 8 inches

The height of the nose of the shortest person that Theodore could lick would be 4 feet 8 inches

b. What is the maximum distance that theodore can stick his tongue out?
d=?
d=sqrt[ (x2-x1)^2+(y2-y1)^2 ]
d=sqrt[ (12 inches - 0)^2+(76 inches-66 inches)^2 ]
d=sqrt[ (12 inches)^2+(10 inches)^2]
d=sqrt(144 inches^2+100 inches^2)
d=sqrt(244 inches^2)
d=sqrt(4x61 inches^2)
d=sqrt(4) sqrt(61) sqrt(inches^2)
d=2 sqrt(61) inches
d=2(7.81) inches
d=15.62 inches

The maximum distance that theodore can stick his tongue out is
2 sqrt(61) inches = 15.62 inches

Bis the correct answer