Problem 292; An Easy Solution 

Professional Surveyor Boards » Problem Corner » Problem 292; An Easy Solution

Name Message
John Nolton
Posts: 15

Joined: 10/11/2011
Topic  Problem 292; An Easy Solution       Flag »  Reply »
The solution that Lindell put forth for problem 292 is long and more complicated than need be.
To solve this problem you need to know 3 things.
1. Heron's formula
2. Pythagorean relation
3.The formula for the altitude (alt) of a general triangle

#1. the area of triangle ABC is K (area)= sqrt s(s-a)(s-b)(s-c) where s= 1/2(a+b+c)
     (this is Heron's formula)
#3. Alt = 2K/side AC
#2. If you don't know this look it up.


Solve for the Area of triangle ABC; s=1/2(6+5+7) , therefore  s= 9
K= sqrt 9(9-5)(9-6)(9-7),  K= 14.696938457
Now Alt of triangle ABC= (2*14.696938457)/7 , therefore Alt= 4.199125273
If we call the foot of the Alt from B to line AC "E" then you will solve 2 triangles using the Pythagorean relation.
First we will solve for distance EC in triangle BEC , EC = sqrt 5^2-Alt^2 , EC=2.714285714.
Now solve for "x" (distance BD in the problem) using the Pathagorean relation again,
DE= 3-EC = 0.285714286 , so x= sqrt DE^2+4.199125273^2; x= 4.208834246

Note: calculations were done on an HP20S calculator and took less than one minute for the solution to the whole problem.

John Nolton
Tombstone, AZ
  Sunday, April 6, 2014 at 1:27:55 PM
20171214yuanyuan
Posts: 152

Joined: 12/14/2017
Reply  Re: Problem 292; An Easy Solution Flag »  Reply »

fred perry polo shirts

uggs outlet

pandora uk

adidas superstars

mbt

michael kors outlet online

michael kors outlet online

ray bans

coach outlet online

ugg outlet

cheap oakley sunglasses

michael kors outlet

canada goose jackets

ralph lauren sale

hermes handbags

  Thursday, December 14, 2017 at 1:03:39 AM
20171214yuanyuan
Posts: 152

Joined: 12/14/2017
Reply  Re: Problem 292; An Easy Solution Flag »  Reply »

superdry

baseball jersey

hollister outlet

air huarache

carnival shoes

nfl jerseys

ralph lauren

nike blazer

swarovski jewelry

michael kors handbags

20186.15wengdongdong
  Thursday, June 14, 2018 at 9:59:29 PM
annajohnsn
Posts: 73

Joined: 3/18/2019
Reply  Re: Problem 292; An Easy Solution Flag »  Reply »
This website is very useful for students like me. washington dc tour We all know the importance of maths in our education system. This site helps the students to learn maths in a very interest way. All the doubts can be discussed here and hence can be solved. I loved the site very much.
  Monday, May 20, 2019 at 6:14:28 AM

Professional Surveyor Boards » Problem Corner » Problem 292; An Easy Solution

 
» Reply to Problem 292; An Easy Solution Topic

In order to post a new message, you must first be logged into an account.