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ArmChairPhysicist
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Please forgive me if I'm in breach of some etiquette with asking for help here, but calculus isn't my strongest subject, and I learn best by example.
I am currently studying in the Life Of Fred Calculus book (do I need to state copyright or something?). I am attempting to work a problem that reads as such:
"Two towers are 120 feet apart. The one on the left is 7 feet tall and the one on the right is 21 feet tall. A beam of light from the top of the left tower bounces off of a lake (note: I assume the lake spans the distance between the two towers, perfectly in line with them and not off somewhere else.) and hits the top of the other tower. Assuming the light takes the shortest path, how far from the base of the left tower will the beam strike the lake?" Authors note: "The algebra- not the calculus- is tough. After you have taken the derivative and set it equal to zero, try x= 10, 20, 30... and one of those will work."
Things I know need to be done.
As the problem states, I'm looking for the length base of a triangle that has 7 feet (the tower) as its height and the beam of light as the hypotenuse. I know I'm going to need the almighty derivative of an equation relating to the triangle, but I'm not sure how to get that equation.
Is there anyone that has experience with this book, or calculus in general, that could help me?
Many thanks in advance for your time.
I am currently studying in the Life Of Fred Calculus book (do I need to state copyright or something?). I am attempting to work a problem that reads as such:
"Two towers are 120 feet apart. The one on the left is 7 feet tall and the one on the right is 21 feet tall. A beam of light from the top of the left tower bounces off of a lake (note: I assume the lake spans the distance between the two towers, perfectly in line with them and not off somewhere else.) and hits the top of the other tower. Assuming the light takes the shortest path, how far from the base of the left tower will the beam strike the lake?" Authors note: "The algebra- not the calculus- is tough. After you have taken the derivative and set it equal to zero, try x= 10, 20, 30... and one of those will work."
Things I know need to be done.
As the problem states, I'm looking for the length base of a triangle that has 7 feet (the tower) as its height and the beam of light as the hypotenuse. I know I'm going to need the almighty derivative of an equation relating to the triangle, but I'm not sure how to get that equation.
Is there anyone that has experience with this book, or calculus in general, that could help me?
Many thanks in advance for your time.
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