At the time that a 55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. Which measure is the closest to the length of the shadow she will cast?
What’s the answer
55/32 = 5.5/x
Cross multiply and solve for x.
its 9.5
To solve this problem, you need to use the concept of similar triangles.
Similar triangles have corresponding angles that are equal and corresponding sides that are proportional. In this case, we have two similar triangles: the triangle formed by the height of the tree, the length of its shadow, and the height of the woman, and the triangle formed by the height of the tree, the length of its shadow, and the length of the woman's shadow.
We can set up a proportion to find the length of the woman's shadow:
(tree height) / (tree shadow length) = (woman's height) / (woman's shadow length)
Plugging in the given values, we have:
55 / 32 = 5.5 / (woman's shadow length)
To find the woman's shadow length, we can solve for it by cross multiplying:
55 * (woman's shadow length) = 32 * 5.5
Finally, we can divide both sides by 55 to find the woman's shadow length:
(woman's shadow length) = (32 * 5.5) / 55
Evaluating the expression, we get:
(woman's shadow length) = 3.2 feet
Therefore, the length of the shadow the woman will cast is closest to 3.2 feet.