# Length of the shadow

## Homework Statement

At the outside, there is a vertical stick with a length of 1.1 meter and its shadow on the surface of an earth is 1.3 meter, there also is light pole and its shadow length is 5.2 meters, what is the height of that light pole?

## Homework Equations

Trigonometry equations to relate height one to height two.

## The Attempt at a Solution

I drew a right triangle, one leg being 1.1 meter, which is the length of a stick, and another leg being 1.3 meter, which is the length of the shadow. Let angle which is between 1.3 meter side and hypotenuse be alpha, so tangent alpha=1.1/1.3. Now I drew another right triangle, one leg being 5.2 meters (shadow length) and another x, which essentially is the height of the light pole. Because light rays emitted from the Sun on the surface of an Earth is almost parallel (because of big distance between the Sun and an Earth), I can say that an angle between 5.2 meters side and hypotenuse will also be alpha, thus x/5.2=1.1/1.3, now solving for x I get 4.4 meters, but I checked the answer and that does not seem to be right answer.

## Answers and Replies

stockzahn
Homework Helper
Gold Member
now solving for x I get 4.4 meters, but I checked the answer and that does not seem to be right answer.

Your answer makes sense, I also calculated 4.4 m. What are a the other possible answers?

• lbwet
Your answer makes sense, I also calculated 4.4 m. What are a the other possible answers?
Other possible answers are:
5.2 m; 5.3 m; 5.5 m; 5.8 m.

And from answers, it says that the correct one is 5.5 m.

haruspex
Science Advisor
Homework Helper
Gold Member
2020 Award
it says that the correct one is 5.5 m.
Clearly 4.4 m is correct.

• lbwet
Clearly 4.4 m is correct.
Thanks, I had doubt but now I'm sure of my answer.