Question 15. Flagpole: A 30m cable is connected to the top of a flag pole....

equate the ratios of hypotenuse to short leg of two similar triangles
 
 
The answer is that the flag pole is 12m from the ground. How do I know this? It was given in the problem.
As an exercise, try finding the height of the shoe (this will make @Harry_the_cat very happy).

EDIT: I just noticed that the OP noted that the height of the shoe is 4m. Very good! However, while the 9.17cm you wrote is fairly close the exact answer should be sqrt(84)
 
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equate the ratios of hypotenuse to short leg of two similar triangles
Sorry to question a post by the infamous @skeeter, I think that it is better to say to equate the ratios of the hypotenuse to the vertical legs of the similar triangles. The reason is that if the two legs of each triangle were close in size then it might confuse the student. On the other hand, the triangles could have been orientated so that there were no horizontal and vertical legs.
Ah, I remember! Say corresponding sides!
 
Wrong (again) Steven! The flag pole is zero metres from the ground, it's the top of the flag pole that is 12 m from the ground. ??

(Another wee trip to the corner for you, eh? )
NOT true! The flag pole occupies space from 0m to 12m from the ground!?
 
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