A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Rex, Paulo, and Ben are standing on the shore watching for dolphins. Paulo sees one surface directly in front of him about a hundred feet away. Use the spaces provided below to prove that the square of the distance between Rex and Ben is the same as the sum of the squares of the distances between Rex and the dolphin, and Ben and the dolphin.
anonymous
 one year ago
Rex, Paulo, and Ben are standing on the shore watching for dolphins. Paulo sees one surface directly in front of him about a hundred feet away. Use the spaces provided below to prove that the square of the distance between Rex and Ben is the same as the sum of the squares of the distances between Rex and the dolphin, and Ben and the dolphin.

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just need help on how to solve the proof

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In general, there is a theorem that would be useful here and perhaps allow the skipping of a couple steps (geometric mean leg theorem if I'm not mistaken). But the proof of that theorem relies on similar triangles, which is what is given in this problem anyway.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know number one is given

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For number 2 would it be AC/BC=BC/AC?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The first reason would be "Given." We are given this information in the problem. The second statement would be: $$\frac{AC}{AB}=\frac{AD}{AC}$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The reason for this is that AC is the hypotenuse of the small triangle. So it corresponds to AB, which is the hypotenuse of the biggest triangle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now, AC is also the smallest side of the biggest triangle, so we want to find the smallest side of the small triangle (ADC). This is AD.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then the third would be b/c=e/b

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. Now crossmultiply. $$\frac{b}{c}=\frac{e}{b}$$ So b^2 = ce

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cross multiply would be the reason for number four. Five is complete. Six is going to be similar to two.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be BC/BA=BD/BC

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For six, it may help to look at seven and work backwards. Yes, you're right. The ratio of the longer leg to the hypotenuse in the biggest triangle equals the ratio of the longer leg to hypotenuse in the secondbiggest triangle.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the reason for six would be the same as that for two. The reason for seven will be the same as that for three. In eight, crossmultiply to get that a^2=cd

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now, if we add the equation in statement four to that in statement eight, we get: $$a^2+b^2=cd+ce$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What would be for number 10 then?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now factor out c on the right side. a^2+b^2 = c(d+e) But d + e is c. So a^2 + b^2 = c*c = c^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The factoring would be number 10.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which is the Pythagorean theorem THANKS!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.