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Any triangle in which the lengths of the sides are in the ratio 3:4:5 is a right triangle.
In general, if a, b, and c are the lengths of the sides of a triangle and a^2 + b^2 = c^2, then the triangle is a right triangle.
In 30°− 60°− 90° triangles, the lengths of the sides are in the ratio 1:sqrt(3):2. For example, in ΔXYZ, if XZ = 3, then XY = 3*sqrt (3) and YZ = 6.
Can anyone explain how in 30-60-90, XY is coming as 3*sqrt(3) ?
In general, if a, b, and c are the lengths of the sides of a triangle and a^2 + b^2 = c^2, then the triangle is a right triangle.
In 30°− 60°− 90° triangles, the lengths of the sides are in the ratio 1:sqrt(3):2. For example, in ΔXYZ, if XZ = 3, then XY = 3*sqrt (3) and YZ = 6.
Can anyone explain how in 30-60-90, XY is coming as 3*sqrt(3) ?
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14 May 2020, 10:54
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Hi ,
This is a general statement : In 30°− 60°− 90° triangles, the lengths of the sides are in the ratio 1:sqrt(3):2.
The values which you have posted for the given XYZ triangle is incorrect. The correct values should be:
XZ=3, XY=3*sqrt(3) , YZ = 6 which conform with the above statement that sides are in ratio 1:sqrt(3):2 .
Please award kudos if you like the solution.
This is a general statement : In 30°− 60°− 90° triangles, the lengths of the sides are in the ratio 1:sqrt(3):2.
The values which you have posted for the given XYZ triangle is incorrect. The correct values should be:
XZ=3, XY=3*sqrt(3) , YZ = 6 which conform with the above statement that sides are in ratio 1:sqrt(3):2 .
Please award kudos if you like the solution.
15 May 2020, 08:50
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skharkia
30:60:90 -> 1:root 3: 2 -> a:a root3:2a,
in ΔXYZ, if XZ = 3, then XY = 3*sqrt (3) and YZ = 6
Now as per above example, xz (30°)= 3 = a, XY (60°)= 3 root 3 =a root 3 and YZ (90°)= 6 = 2a.
so, here a =3.
Similarly, 45° - 45° - 90° triangle have side ratio as a:a:a root 2.
