IIT JEE , AIEEE Forum - Mathematics , Trignometry

VINAY_111

If the angles of a triangle are in the ratio 2 : 3 : 5, then the ratio of the greatest side to the least side is ?

malay

angles will be 36, 54,90
hence required ratio will be sin90/sin36

aysh

let the angles be 2x, 3x and 5x.
Then,
2x + 3x + 5x=180
Thus,
x=18
Now the grestest side will have the greatest angle opposite 2 it and the shortest side will have the smallest angle opposite 2 it.
Let the triangle be ABC with A as its largest angle(5x) and C as its smallest angle(2x).
Therefore,
by applying the law of sines, we get
a/c = sinA / sinC
a/c = sin5x / sin2x
a/c = sin90 / sin36
a/c = 4 / {10-2(5)^1/2}^1/2
[4 by root{10-2root(5)}]

PLEASE RATE PEOPLE....

sibin15

The angles will be 36,54 and 90

then From sine rule a/sina=b/sinb=c/sinc

we can get the ratio of the sides

thanx

KraniuM

er..... vel, the angles vill be 36,54 and 90 as explaind above,......so, it is a right angled triangle, the greatest side vill be the hypotenuse and the least side vill be opposite 36 degrees, that is, 1/cos54

i.e. sec54.

am i rite???

iitkgp_bipin

Let the angles be 2x,3x,5x

2x + 3x + 5x = 180⁰

x = 18⁰

Hence the angles are 36⁰,54⁰,90⁰

By sine rule ratio of (greatest side : least side) = sin90⁰/sin36⁰ = cosec36⁰

choudhari.mayur

let the angles be 2x, 3x and 5x.
Then,
2x + 3x + 5x=180
Thus,
x=18
Now the grestest side will have the greatest angle opposite 2 it and the shortest side will have the smallest angle opposite 2 it.
Let the triangle be ABC with A as its largest angle(5x) and C as its smallest angle(2x).
Therefore,
by applying the law of sines, we get
a/c = sinA / sinC
a/c = sin5x / sin2x
a/c = sin90 / sin36
a/c = 4 / {10-2(5)^1/2}^1/2
[4 by root{10-2root(5)}]

PLEASE RATE PEOPLE....

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