Amelia is 5 feet tall and casts a 4-foot shadow.
A tree next to her casts a 12-foot shadow.
The two triangles formed are similar because the angle to the sun is the same.
Choose two equations that can be used to find the height, h, of the tree.
IM CONFUSED
12/4=h/5
5/4=h/12
i had the same question on ttm and I got it right :)
To find the height, h, of the tree, we can use the concept of similar triangles. Here's how you can set up the equations:
1. Using the ratios of corresponding sides:
In similar triangles, the ratios of corresponding sides are equal. Since the triangles formed by Amelia and her shadow are similar to the triangles formed by the tree and its shadow, we can set up the following equation:
(h/t) = (5/4)
where h represents the height of the tree and t represents the length of the tree's shadow.
2. Using the angle of elevation:
Since the two triangles are similar because the angle to the sun is the same, we can use the concept of the angle of elevation to set up another equation. The angle of elevation is the angle between the ground and the line of sight to the top of an object.
tan(angle) = opposite/adjacent
In this case, the angle of elevation can be found by taking the inverse tangent of the ratio of the lengths of Amelia's shadow and her height:
tan(angle) = 4/5
Then, we can use the angle of elevation and the length of the tree's shadow to find the height of the tree:
tan(angle) = h/t
Combining these two equations, we have:
h/t = tan(angle) = 4/5
These are two equations that can be used to find the height, h, of the tree using the given information.
h/12 = 5/4
h/5 = 12/4
or even
12/√(h^2+144) = 4/√41
12/√(h^2+144) = 4/√41 ?
Reminds me of a Walt Disney math movie called
Donald Duck in Mathemagics Land, where he is in a forest where all
the trees have square roots.
h = Height of the tree
5 / 4 = h / 12
Cross multiply
5 ∙ 12 = h ∙ 4
60 = 4 h
4 h = 60
h = 60 / 4
h = 15 ft
OR
Foot´s shadow = 12 ft
Amelia´s shadow = 4 ft
12 ft / 4 ft = 3
The two triangles formed are similar so the height of the tree is 3 times higher than Amelia's height.
Height of the tree = 3 Amelia's height
h = 3 ∙ 5 ft = 15 ft