how tall is a tree that casts a 25-ft shadow at the same time a 9-ft light pole casts a 15-ft shadow?

Answer 1

setting up two tangents that are equal (because the sun is the same height...)

tan Θ = x/25
tan Θ = 9/15
equate them

x/25=9/15
x/5=9/3
x/5=3
x=15 ft

Answer 2

We don't need angles and such to work this problem All we need to know is that the tree and the light post, and their respective shadows for similar right triangles. The shadows are the x axis sides and the heights of each are the y axis sides.

Because they are similar triangles the ratios of their heights to shadows are the same. Thus, h/s = H/S; where h = height of the light pole, s = its shadow length, H = the height of the tree, and S is its shadow. So we have H = h(S/s) = 9(25/15) = 9(5/3); you can do the math.

Lesson learned: Similar triangles (having the same shape but not necessarily the same size) will have the same ratio of their corresponding sides no matter how big or small those similar triangles might be.

PS: Since the tree shadow is bigger than the pole shadow, you must know that the tree is taller than the pole. Any answer to the contrary is clearly incorrect.

Answer 3

it is not too puzzling. you're making a ratio of the area lengths: 9 ft / 15 ft = x ft / 25 ft, then sparkling up for x. it extremely works by way of fact the shadows are being solid on the comparable time, so which you have comparable triangles. meaning the ratios of their area lengths may be the comparable.

Answer 4

What's a light pole? Is it the thing that provides the light that is making the shadow of the tree?

Answer 5

Using the program in the proof, the tree is 15 ft tall. Use SOH CAH TOA to find these answers.

Answer 6

9/15 = 3/5
3/5 = x/25

x=15

Answer 7

It's a simple ratio question. 9 is to 15 as x is to 25.
9/15 * 25 = 15 feet.

Answer 8

15 feet.

Answer 9

I go with the first guy on this one