answersLogoWhite

0


Best Answer

tan (A-B) + tan (B-C) + tan (C-A)=0

tan (A-B) + tan (B-C) - tan (A-C)=0

tan (A-B) + tan (B-C) = tan (A-C)

(A-B) + (B-C) = A-C

So we can solve

tan (A-B) + tan (B-C) = tan (A-C)

by first solving

tan x + tan y = tan (x+y)

and then substituting x = A-B and y = B-C.

tan (x+y) = (tan x + tan y)/(1 - tan x tan y)

So tan x + tan y = (tan x + tan y)/(1 - tan x tan y)

(tan x + tan y)tan x tan y = 0

So, tan x = 0 or tan y = 0 or tan x = - tan y

tan(A-B) = 0 or tan(B-C) = 0 or tan(A-B) = - tan(B-C)

tan(A-B) = 0 or tan(B-C) = 0 or tan(A-B) = tan(C-B)

A, B and C are all angles of a triangle, so are all in the range (0, pi).

So A-B and B-C are in the range (- pi, pi).

At this point I sketched a graph of y = tan x (- pi < x < pi)

By inspection I can see that:

A-B = 0 or B-C = 0 or A-B = C-B or A-B = C-B +/- pi

A = B or B = C or A = C or A = C +/- pi

But A and C are both in the range (0, pi) so A = C +/- pi has no solution

So A = B or B = C or A = C

A triangle ABC has the property that tan (A-B) + tan (B-C) + tan (C-A)=0 if and only if it is isosceles (or equilateral).

User Avatar

Wiki User

โˆ™ 2012-06-06 15:50:46
This answer is:
๐Ÿ™
0
๐Ÿคจ
1
๐Ÿ˜ฎ
0
User Avatar
Study guides
๐Ÿ““
See all Study Guides
โœ๏ธ
Create a Study Guide

Add your answer:

Earn +20 pts
Q: If for a triangle abc tan a-b plus tan b-c plus tan c-a equals 0 then what can you say about the triangle?
Write your answer...
Submit
Related questions

2 plus 3 equals 10 7 plus 2 equals 63 6 plus 9 equals 66 8 plus 4 equals 96 what is 9 plus 7 equals?

2 plus 3 equals 5 7 plus 2 equals 9 6 plus 9 equals 15 8 plus 4 equals 12 9 plus 7 equals 16 Am I missing something here? Probably. You say 2+3=5, but the question clearly states 2+3=10. Why would it say that? Suppose you had only one hand. You count 1,2,3,4,5,10,11,12. That last doesn't mean "twelve" as we know it, Jim. It means one hand (5), plus 2 spare ones. We could say: if 2+3=10, 5+2=12.


-x plus 3y equals 1?

there is a multitude of answers to that. Let's say Y equals 2 and X equals 5. So -5 plus 3(2)= 1


How is a triangle classified as a right triangle?

The formula is A2 + B2=C2. Say if 102 +102=202.The hypotenuse is 202.So 102 +102=200.And 202=200. the triangle is a right triangle. It equals the hypotenuse.


What can you say about the graph Ax plus By equals C about the graph Ax plus By equals C?

It is a straight line with gradient -A/B and intercept C/B.


How do you say 4 plus 1 equals 5 in German?

vier plus eins ist funf


If A plus B equals 0 what can you say about the components?

they are additive inverses


When was Say It - ABC song - created?

Say It - ABC song - was created in 1992-01.


Why do people say that nine plus ten equals twenty one?

because it does say its Twenty OnE


How do you say 5 plus 5 equals 10?

5 + 5 = 10


How do you say 10 plus 9 equals 19 in Spanish?

Google translator converts 'ten plus nine equals nineteen' to Spanish as 'diez mรกs nueve es igual a diecinueve'


How do you say triangle in french?

triangle


How do you simultaneously solve 7C plus 6H equals 2500 and 13C plus 1H equals 2310 any help?

Get two slaves. Give one equation to each slave. Say, "Go!"


Is 8 plus 2 a statement?

Yes, but on ly if you don't say "equals 10 " at the end.


If a plus b equals 0 what can you say about the component?

That a and b are additive inverses of one another.


Is the Bermuda triangle really a triangle?

we can say somehow it is triangle the area which it covers is Bermuda Miami and ruerto Rico so it we can say its not a perfect triangle.


How do you say ABC in German?

Alphabet.


How do you say triangle in Spanish?

Triangle in Spanish is tri&aacute;ngulo.


How-to structure in c plus plus?

A structure in C++ is nearly the same as a structure in C. struct abc { int item1; int item2; ... etc... } mystructure; There are several differences. Two examples are... In C++, you get automatic typedef'ing, so that (in this example) you would not have to say struct abc mysecondstructure; - you can just say abc mysecondstructure;. In C++, structures are very similar to classes. In fact, structures are classes, which is why you get automatic typedef'ing.


What will 7ai6464 2a87 a63 3647 say if the answer key said 2 equals abc 3 equals def 4 equals ghi 5 equals jkl 6 equals mno 7 equals pqrs 8 equals tuv and 9 equals wxyz?

The telephone keypad is the clue to the answer.7ai64364 2a87 a6e 3647raining cats and dogs


Does x plus 5 divided by 5 plus x equal 1?

No. In the order of operations, 5 divided by 5 comes first. Let's say x equals 2. 2 plus 5 divided by 5 plus two 2 plus 1 plus 2 3 plus 2 equals 5. The answer is 5


What did the triangle say to the circle?

wawawawawawawawawa


What is y equals -4x plus -7?

-11


Who said Freedom is the ability to say 2 plus 2 equals 4?

George Orwell's character Winston in 1984.


Is a triangle a scalene triangle?

i'm not sure, but I would say yes.


How long are each sides of an equilateral triangle if the perimeter is 60?

20. There are 3 sides to any triangle. For an equilateral triangle all 3 sides are the same length. Therefore for this triangle we can say that, where x equals the length of a side: 3x = 60 x = 60/3 x = 20