To measure the height of a tree, we can use the length of its shadow and the length of our own shadow at the same time. If the shadow of the tree is 13 feet and 11 inches long when we cast a shadow 2 feet and 8 inches long, and we are 5 feet and 10 inches tall, then the height of the tree can be found using the following formula:
Tree height = (length of person's shadow x height of tree) / length of person
Plugging in the values, we get:
Tree height = (2.67 x height of tree) / 5.83
Simplifying, we get:
Tree height = 0.457 x height of tree
To solve for the height of the tree, we can divide both sides by 0.457:
Height of tree = Tree height / 0.457
Plugging in the length of the tree's shadow and our shadow, we get:
Height of tree = (13 x 12 + 11) x 5.83 / (2 x 12 + 8) = 111.83 inches
Therefore, the height of the tree is approximately 9 feet and 4 inches.