Question

A certain time of day, the length of the shadows cast on the ground by two different height trees are shown in the table. Given this information, if a third tree cast a shadow 70 feet long., how tall is the tree in feet? a)15 b)20

Answer 1

To find the height of the third tree, use the concept of similar triangles. Set up a proportion comparing the height to the shadow length of the first tree. Then, solve for the height of the third tree using the given shadow length.which is approximately 93.3 feet.

Step-by-step explanation:

To find the height of the third tree, we can use the concept of similar triangles. We can compare the ratio of the height of the first tree to its shadow length with the ratio of the height of the third tree to its shadow length.

Let's consider the first tree, which has a shadow length of 30 feet and a height of 40 feet. The ratio of the height to the shadow length is 40/30 = 4/3.

Now, we can set up a proportion: (height of the third tree)/(shadow length of the third tree) = 4/3. Given that the shadow length of the third tree is 70 feet, we can solve for the height of the third tree: (height of the third tree)/70 = 4/3.

Cross-multiplying and solving for the height of the third tree, we get (height of the third tree) = (70 x 4)/3 = 280/3 feet, which is approximately 93.3 feet.