Answer: 23.2 ft
Step-by-step explanation:
The comparison is height to shadow, so the ratios can be written as height/shadow. One ratio represents the tree while the other represents the boy. The unknown value is the height of the tree, so x will fall in the numerator.
Find the cross products, set them equal, and simplify.
x/38=5.5/9
9⋅x=38⋅5.5
9x=209
Divide both sides by 9 to isolate the variable x.
x=23.2
Based on the height of the boy relative to the tree, the height of the tree is 23.2 feet tall.
The boy is 5.5 feet tall and yet the shadow was 9 feet in length. There is therefore a scale here that can be calculated by:
= Height of shadow / Height of boy
= 9 / 5.5
= 1.64
We can use this to find the height of the tree as:
= Height of tree shadow / Scale of increase
= 38 / 1.64
= 23.2 feet
In conclusion, the tree is 23.2 feet tall.
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