What is the relation between the angles and side lengths of a triangle?

Answer 1

the larger the angle, the longer the opposite side. the smallest angle in a triangle has the shortest opposite side; the largest angle has the longest opposite side

Answer 2

The angles of a triangle are in the same proportion as the length of its sides. For example:

(1) The sum of the measures of any pair of sides in a triangle will always be greater than the measure of the remaining side.
[s + m > l]

(2) The longest side of a triangle will always be opposite the greatest angle of the triangle, and the shortest side will always be opposite the smallest angle.
[Given ΔABC with m∠A > m∠B > m∠C, we know that BC > AC > AB.]

Answer 3

The measurements which you supply are component to a touch in call for genuine-perspective triangle. 3,4,5 make up the the desirable option, backside, and hypothenuse of a real triangle. the perspective at vertex C is ninety levels. the perspective at A is inv-sin(4/5) and the perspective at B is inv-sin(3/5). yet another in call for triangle has lengths a million,2,sqrt(3). That has angles 30,60, and ninety levels. to sparkling up for the ordinary triangle once you have in simple terms the lengths of the two aspects, you need to use the regulation of cosine: c^2 = a^2 + b^2 - 2*a*b*cosine(C) Plug in a, b, and c, then sparkling up for perspective C you are able to word a similar equation for different 2 angles. Use A+B+C = one hundred eighty levels as verification.

Answer 4

according to sine rule:
the triangle ABC having angles A ,B ,C and sides a,b,c i.e,
a being the side length of side opposite to the angle A and the same for b,B and c,C.
and R as the circumradius of the triangle ABC.
the relation is a/sinA = b/sinB = c/sinC = 2R.

Answer 5

A good relationship is the law of sines. If ABC is a triangle, and a is the angle opposite the angle A, etc. then:

sin(A)/a = sin(B)/b = sin(C)/c

Answer 6

The square of the hypotenuse (the side opposite the angle) is equal to the the sum of the squares of the other two sides (the opposite and the adjacent) The angles are the sine of the opposite over the hypotenuse, the cosine of the adjacent over the hypotenuse, and the tangent of the opposite over the adjacent. I think (off the top of my head.) Look it up on the Internet to confirm.

Answer 7

if in a triangle ,any 2 angles are same then the lenghts of their opposite sides are also same.

Answer 8

consider a,b,c be sides of triangle
and A,B,C be angle opp. to corresponding sides

SinA / a = SinB / b = SinC / c

and
cos A= (b^2+c^2-a^2)/b*c

Answer 9

we can say , there is no relation between angles and side lengths of triangle.but the relation is between the
ratio aof sidelengths and angles

Answer 10

Relationshp of proximity above all.