A tree casts a shadow 25 m long. At the same time, the shadow cast by a 57-cm tall statue is 66 cm long. Find the height of the tree to the nearest meter.
h/25=.66/.57
A point lies on the of a line segment if and only if the point is equidistant from the endpoints of the segment.
angle bisector
trisector
altitude
perpendicular bisector
To find the height of the tree, we can use the concept of similar triangles.
Let's assume the height of the tree is h meters and the height of the statue is s meters.
We can set up a proportion using the lengths of the shadows and the heights of the objects:
(length of tree's shadow) / (height of tree) = (length of statue's shadow) / (height of statue)
In this case, we have the following values:
(length of tree's shadow) = 25 meters
(length of statue's shadow) = 66 centimeters = 0.66 meters
(height of statue) = 57 centimeters = 0.57 meters
Let's substitute these values into the proportion:
25 / h = 0.66 / 0.57
To solve for h, we can cross multiply:
0.57 * 25 = 0.66 * h
14.25 = 0.66 * h
Dividing both sides by 0.66, we can find the value of h:
h = 14.25 / 0.66
h ≈ 21.59 meters
Therefore, the height of the tree is approximately 21.59 meters.