Question

At 3 pm., Coretta's shadow is 1.03 meters long. Her height is 1.66 meters. At the same time, a tree's shadow is 6.57 meters long. How tall is the tree?

Answer 1

By using similar triangles, the height of the tree is calculated to be approximately 10.26 meters tall.

Step-by-step explanation:

At 3 pm., Coretta's shadow is 1.03 meters long, and her height is 1.66 meters. Similarly, a tree's shadow is 6.57 meters long at the same time, and we are interested in finding out the height of the tree. This problem can be solved using similar triangles, which means that the ratio of Coretta's height to her shadow length should be the same as the ratio of the tree's height to its shadow length.

So, we set the ratios equal to each other

• Coretta's Height / Coretta's Shadow = Tree Height / Tree's Shadow
• 1.66 m / 1.03 m = Tree Height / 6.57 m

To find the Tree Height, we cross-multiply and solve for it:

• (Tree Height) * (1.03 m) = (1.66 m) * (6.57 m)
• Tree Height = (1.66 m * 6.57 m) / (1.03 m)
• Tree Height = 10.5712 m / 1.03 m
• Tree Height ≈ 10.26 m

The tree is approximately 10.26 meters tall.