In triangle PQR , angle Q = 40 degree and angle R = 72 degree , then find the shortest and longest sides of the triangle .
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angle Q = 40 deg angle R = 72 deg
So we get that the angle P = 68 deg
Let the smallest side be = q. longest side be r . and the other be p. Let the radius of the circumcircle be R.
a/Sin A = b/SinB = c/sinC = 2 R
So the ratio: r/q = sin 72° / sin 40°
There will be infinite number of triangles (similar) with the given angles. So the lengths of sides r and q are not unique. The ratio is unique as above.
So we get that the angle P = 68 deg
Let the smallest side be = q. longest side be r . and the other be p. Let the radius of the circumcircle be R.
a/Sin A = b/SinB = c/sinC = 2 R
So the ratio: r/q = sin 72° / sin 40°
There will be infinite number of triangles (similar) with the given angles. So the lengths of sides r and q are not unique. The ratio is unique as above.
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