smallest angles of what? a triangle?
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It depends on whether the ratio refers to the angles of the triangle or the length of the sides.
1 Using the fact that: The square root of (x1-x2)2+(y1-y2)2 = length of line2 Line lenth of: (5, 9) and (14, -3) = 15 (hypotenuse)3 Line length of: (14, -3) and (2, 3) = 6*sq rt of 5 (opposite)4 Line length of: (2, 3) and (5, 9) = 3*sq rt of 5 (adjacent)5 Smallest angle: tan-1(6*sq rt of 5) over (3*sq rt of 5) = 26.6 degees to 1 d.p.6 Check: (6*sq rt of 5)2+(3*sq rt of 5)2 = 225 and its square root is 15 which is the length of the hypotenuse of the right angle triangleIn any triangle, the smallest angle is opposite to the shortest side.
The three basic ratios are sine, cosine and tangent.In a right angled triangle,the sine of an angle is the ratio of the lengths of the side opposite the angle and the hypotenuse;the cosine of an angle is the ratio of the lengths of the side adjacent to the angle and the hypotenuse;the tangent of an angle is the ratio of the lengths of the side opposite the angle and the the side adjacent to the angle.
The ratio of the lengths of the hypotenuse to the shortest side is 2, and the ratio of the lengths of the two sides adjacent to the right angle is the square root of 3.
The ratio 3 to 2 is equal to 1.5.