Question

a giraffe is looking down at a bag of peanuts while a boy, sitting on his dad’s shoulders, is looking up at the giraffe. the distance from the ground to the giraffe’s eyes is 12 feet, and the giraffe is 48 feet away from the bag of peanuts. the diagram is illustrated using similar triangles. note: image not drawn to scale the boy and his dad are 28 feet away from the bag of peanuts. the height of the boy and his dad is □ feet.

Explanation:

Step1: Identify similar triangles

We have two similar right triangles. Let \( h \) be the height of the boy and his dad. The larger triangle has height 12 ft and base 48 ft. The smaller triangle has height \( h \) and base 28 ft.

Step2: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal: \(\frac{h}{28}=\frac{12}{48}\)

Step3: Solve for \( h \)

Cross - multiply: \( 48h = 12\times28 \)
Calculate \( 12\times28 = 336 \)
Then \( h=\frac{336}{48}=7 \)

Answer:

7