A person that is 1.6 m tall casts a 4 m shadow. At the same time, a nearby tree casts a 12 m shadow. What is the height of the tree to the nearest tenth of a metre?
1.6:4=n:12 or 1.6/4=n/12
(12*1.6)/4=n, so what is n?
4.8 m.
Drawing a picture for this problem creates two similar triangles, you simply have to use the given ratio from the first triangle to find the height of the tree, so 1.6/4=x/12. Cross-multiplying gives us (1.6)(12)=4X, Therefore, x=((1.6)(12))/4
To find the height of the tree, we can use a proportion. We can set up the proportion:
Person's height / Person's shadow = Tree's height / Tree's shadow
Let's plug in the given values:
1.6 m / 4 m = Tree's height / 12 m
Now, we can cross-multiply to solve for the tree's height:
(1.6 m) * (12 m) = 4 m * Tree's height
19.2 m = 4 m * Tree's height
To isolate the tree's height, we can divide both sides of the equation by 4 m:
19.2 m / 4 m = Tree's height
4.8 m = Tree's height
So, the height of the tree is approximately 4.8 meters.