Tree casts a shadow 30 feet long. A MHS student standing near the tree casts a shadow 9 feet long. The student is 6 feet tall. What is the height of the tree? Show all work
Answer:
Option D
The height of tree is 20 feet tall
Solution:
From given question,
Shadow of tree = 30 feet
Height of tree = ?
Height of student = 6 feet
Shadow of student = 9 feet
We have to find the height of tree
We can solve the sum by proportion
[tex]\frac{\text{height of tree}}{\text{shadow of tree}} = \frac{\text{height of student}}{\text{shadow of tree}}[/tex]
This forms a proportion and we can solve the sum by cross multiplying
[tex]\frac{\text{height of tree}}{30} = \frac{6}{9}\\\\\text{height of tree} = 30 \times \frac{6}{9} = 30 \times \frac{2}{3}\\\\\text{ height of tree } = 10 \times 2 = 20[/tex]
Thus height of tree is 20 feet tall
