Final answer:
To find the distance of the thumb to ring finger in the shadow, use the similar triangles principle. With the hand 12 inches away from the light and 60 inches away from the wall, the shadow's length is calculated to be 30 inches.
Step-by-step explanation:
The student asks how to find the distance between the thumb and ring finger in the shadow when a hand is held 1 foot from a flashlight and 5 feet from a wall. This problem involves similar triangles because the hand and its shadow will form two similar triangles when light is projected onto the wall.
The question will be solved using the concept that the ratios of corresponding sides of similar triangles are equal. This means that the shadow's size is proportional to the distance from the light source:
Length of hand's shadow / Length of hand = Distance from wall to the light source / Distance from hand to the light source
Given that the distance from the hand to the light source is 1 foot (12 inches) and the distance from the wall to the light source is 5 feet (60 inches), and the actual hand width is 6 inches, we can set up a proportion and find the length of the shadow:
Shadow's Length / 6 inches = 60 inches / 12 inches
Shadow's Length = (6 inches * 60 inches) / 12 inches
Shadow's Length = 30 inches. Therefore, the distance of the thumb to ring finger in the shadow is 30 inches.