A building is 51 ft tall and casts a shadow 48 ft long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue?

eddy2017

eddy2017

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Hi, dea friends and teachers: I keep studying little by little in my free time which is not much. i thank you from the bottom of my heart for your help
here's a problem that i am trying to understand, that is real difficult for my level. I am posting here in hopes that you give me the useful hints you give and see if i can understand the logic and reasoning behind every step. Thanks a lot,
eddy

A building is 51 ft tall and casts a shadow 48 ft long. Simultaneously, a nearby statue casts a shadow of 16 feet. How tall is the statue?
 
Because the sunlight is at the same angle for each, and presumably the ground is level, the shadows form similar triangles. Write a proportion and solve for the unknown height.

If that is not enough, please show us your drawing and your work, so we can tell what help you need.

Also, tell us what your level is -- what are you currently learning? I would guess it is either similar triangles or proportions!
 
Thanks for helping!. I am prepping for math subject area from 5 to 9, ( it will be a long and hard battle but i will get there) but struggling with word problems.
setting up proportions
I get the first proportion from the height of the building and the measurements of the shadow it projects.
in the second proportion, i have the the length of the shadow, but the height is what is missing, the unknown value, that i choosoe to represent by h( h for height)
51/48= h/16
i do the cross multiplication
isolate the variable and i get that h= 17 ft
How tall is the statue? . it is 17 ft tall
What do you think?
One question, if i may, is there any rule in deciding what measurement to put on top and which one goes in the bottom, when setting up my first proportion?
Thanks a lot,
 
eddy2017 said:
Thanks for helping!. I am prepping for math subject area from 5 to 9, ( it will be a long and hard battle but i will get there) but struggling with word problems.
setting up proportions
I get the first proportion from the height of the building and the measurements of the shadow it projects.
in the second proportion, i have the the length of the shadow, but the height is what is missing, the unknown value, that i choosoe to represent by h( h for height)
51/48= h/16
i do the cross multiplication
isolate the variable and i get that h= 17 ft
How tall is the statue? . it is 17 ft tall
What do you think?
One question, if i may, is there any rule in deciding what measurement to put on top and which one goes in the bottom, when setting up my first proportion?
Thanks a lot,
Click to expand...
Good work.

A quicker method, in this case, is to see that in 51/48= h/16, 48 = 3*16, so 51 = 3*h, so that h = 51/3 = 17. But that's only quicker when you don't use a calculator!

In general, the important thing is to match up corresponding parts. Here, you are using height/shadow for both triangles.

Often, if you can put things in a table, that effectively turns into your proportion:

Code: 
         height  shadow
         ------  ------
building   51      48
statue      h      16

You can write this either as 51/h = 48/16, or as 51/48=h/16.
 
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