John is standing in his backyard and decides to estimate the height of a tree. He stands so that the tip of his shadow coincides

Question

3 years ago

14

John is standing in his backyard and decides to estimate the height of a tree. He stands so that the tip of his shadow coincides

with the tip of the tree's shadow, as shown below. John is 70 inches tall. The distance from the tree to John is 75 feet and the distance between the tip of the shadows and John is 7
feet. About how tall is the tree, to the nearest foot? Be careful with your units!!!

Mathematics

1 answer:

Andrew [12] · Answer 1 · 2022-09-24T20:00:39+03:00

The tree is 820 inches tall using the similarity of triangles.

To get the height of the tree, we will use the properties of similar triangles expressed as:

$\frac{70in}{7ft} = \frac{h}{75ft+7ft}\\\frac{70in}{7ft} = \frac{h}{82ft}\\$

Note that 1 foot = 12inches

7ft = 84in and 82ft = 984in

h is the required height of the tree. Simplify the equation above to get the height "h" and replace feet with inches;

$\frac{70}{84} = \frac{h}{984}\\84h =70 \times 984\\84h = 68,880\\h=\frac{68,880}{84}\\h= 820in$

Hence the tree is 820 inches tall using the similarity of triangles.

Learn more on similarities of triangles here: brainly.com/question/24295402