A palm tree that is 32 feet tall, casts a shadow that is 26 feet long. Matt is 6 feet tall and standing near the palm tree. Use the figure above to determine the length of Matt’s shadow. Round to the nearest tenth.
Why did the palm tree invite Matt to stand near it? Because it wanted to overshadow him with its impressive height! Now, let's calculate the length of Matt's shadow. Since we know that the palm tree is 32 feet tall and casts a shadow that is 26 feet long, we can set up a proportion:
Palm tree height / Palm tree shadow length = Matt's height / Matt's shadow length
Plugging in the given values:
32 / 26 = 6 / Matt's shadow length
Now we can solve for Matt's shadow length:
Matt's shadow length = (6 * 26) / 32
Calculating this out:
Matt's shadow length ≈ 4.875 feet
So, Matt's shadow is approximately 4.9 feet long when he is standing near the palm tree.
To find the length of Matt's shadow, we can use the concept of similar triangles. We know that the height of the palm tree is 32 feet, and its shadow is 26 feet long.
Let's call the length of Matt's shadow x.
Using the concept of similar triangles, we can set up the following proportion:
height of palm tree / length of palm tree shadow = Matt's height / length of Matt's shadow
32 / 26 = 6 / x
Cross-multiplying, we get:
32x = 156
Solving for x, we get:
x = 156/32
x ≈ 4.875
Therefore, the length of Matt's shadow is approximately 4.9 feet (rounded to the nearest tenth).
To determine the length of Matt's shadow, we can set up a proportion using the similar triangles formed by the palm tree, its shadow, and Matt's height and shadow.
Let's define:
P = height of the palm tree (32 feet)
PS = length of the palm tree's shadow (26 feet)
M = height of Matt (6 feet)
MS = length of Matt's shadow (unknown)
We can set up the proportion using the corresponding sides of the triangles:
(PM / PS) = (M / MS)
Substituting the given values:
(32 / 26) = (6 / MS)
To solve for MS, we can cross-multiply and then divide to isolate MS:
32 * MS = 26 * 6
32 * MS = 156
MS = 156 / 32
Calculating MS:
MS ≈ 4.875 feet
Therefore, according to the proportion, the length of Matt's shadow is approximately 4.9 feet.
No figure above, but probably the typical problem where
32/26 = 6/x
32x= 6*26
etc