Use similar triangles to solve. A person who is 5 feet tall is standing 117 feet from the base of a tree, and the tree casts a 130 foot shadow. The person's shadow is 13 feet in length. What is the height of the tree?
Add 117+13 giving you 130
130/13 = X/3 cross multiply
130*5= 13x
650=13x
x=50
height of the tree is 50 ft
x/5*
Well, this sounds like a rather shady situation! Let's figure it out using some similar triangles.
We have two triangles here – one formed by the person, their shadow, and their distance from the tree, and the other formed by the tree, its shadow, and the same distance from the tree. Since these two triangles are similar, their corresponding sides are proportional.
Now, we know that the person's height is 5 feet and their shadow is 13 feet. The distance from the person to the tree is 117 feet, and the tree's shadow is 130 feet.
So, let's set up a proportion: (person's height) / (person's shadow) = (tree's height) / (tree's shadow)
Substituting the given values, we get: 5 / 13 = (tree's height) / 130
Now, let's solve for the tree's height. Cross-multiplying, we get: 5 * 130 = 13 * (tree's height)
Simplifying, we have: 650 = 13 * (tree's height)
Dividing both sides by 13, we find: (tree's height) = 650 / 13
Calculating that, we get: (tree's height) ≈ 50 feet
So, it looks like the height of the tree is approximately 50 feet! We've finally reached the top of this little mathematical forest!
To solve this problem using similar triangles, we need to understand the concept of similar triangles and their proportionality.
Similar triangles are triangles that have the same shape but possibly different sizes. The corresponding angles in similar triangles are equal, and the ratio of corresponding side lengths is constant.
In this problem, we can see that there are two triangles involved: the triangle formed by the person, their shadow, and their height, and the triangle formed by the tree, its shadow, and its height.
Let's label the height of the tree as 'h' and its shadow as 's'. Similarly, we can label the height of the person as 'x' and their shadow as 'y'.
Based on the information given, we know that the person's height is 5 feet, their shadow is 13 feet, the person is standing 117 feet from the tree, and the tree's shadow is 130 feet.
Now, we can set up a proportion using the corresponding sides of the two triangles:
(person's height) / (person's shadow) = (tree's height) / (tree's shadow)
This can be written as:
5 / 13 = h / 130
To find the height of the tree 'h', we can solve this proportion for 'h' by cross-multiplying:
5 * 130 = 13 * h
650 = 13h
Now, we can solve for 'h' by dividing both sides of the equation by 13:
h = 650 / 13
Finally, we find that the height of the tree is:
h = 50 feet.
Draw the diagram. This is exactly like "Isel's" problem.
h/130 = 5/13