Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft lo...

Question

Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30-ft tree be at the same time and place?

Accepted Answer

Hello, everyone from the top of a lighthouse standing 249 ft above sea level, water is shot at an angle downward and travels 338 ft until it reaches the ground. Ignoring air resistance, determine how far the water travels for a 271 ft lighthouse at the exact same moment and location. Our answer choices are a 368 ft. B 311 ft C 200 ft D 297 ft. So we're gonna set up a proportion and recall that a proportion is two fractions that are equal to each other. So I'm gonna have what I'm gonna call lighthouse A and lighthouse B and each lighthouse will have its own fraction. So lighthouse A is what I'm calling my first lighthouse. So I'm gonna put the height of the lighthouse divided by the distance the water travels. And I'm gonna just denote that as water and that's gonna be set equal to the height of lighthouse B divided by the distance that water travels. So now let's see what we can find to fill in. For numbers, lighthouse A we are told is 249 ft above sea level. So that's what I'm gonna call the height. We're gonna divide that by the distance the water travels for lighthouse A or our first lighthouse which is 338 ft. Lighthouse B we're told is 271 ft and we don't know how far the water travels. So our denominator of our second fraction is X. So now that we have a proportion set up, we can solve this by cross multiplying. So we multiply diagonally across the equal sign. So 249 multiplied by X is 249 X and then 338 multiplied by 271 is 91,598. And then to solve for X, we divide both sides by 249. And when we do, we get that X equals 367.863 it appears all of our answer choices have been rounded to the nearest foot. So when I do that here, we find that the distance the water travels from our second lighthouse which I called lighthouse B would be 368 ft and 368 ft is answer choice. A have a nice day.

Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, how long would the shadow of a 30-ft tree be at the same time and place?

Key Concepts

Similar Triangles

Proportionality in Right Triangles

Application of Ratios

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