a student measures the height of a sign to be 2 meters. the shadow of the sign 3 meters. the student notices that at the same time nearby tree has a shadow of 15.6 meters. how tall is the tree? What equation would be used for this?
Use a proportion.
2/3 = x/15.6
Cross multiply and solve for x.
To find the height of the tree, we can use the concept of similar triangles and the ratios of corresponding sides. We can set up a proportion using the height of the sign, shadow length of the sign, shadow length of the tree, and the unknown height of the tree.
Let's set up the proportion:
Height of the sign / Shadow length of the sign = Height of the tree / Shadow length of the tree
Substituting the given values:
2 meters / 3 meters = Height of the tree / 15.6 meters
To solve for the height of the tree, we can cross-multiply and then divide:
(2 meters) x (15.6 meters) = 3 meters x Height of the tree
31.2 = 3 x Height of the tree
Divide both sides of the equation by 3:
31.2 / 3 = Height of the tree
Therefore, the height of the tree is approximately 10.4 meters.