Short leg = x
Long leg = x times the square root of 3
Hypotenuse = 2x
the ratios in such a triangle are 1:2:sqrt(3) so the longest length is opposite the 90 degree angle and is twice as large as the length opposite the 30 degree angle
The longer leg is opposite the 60 deg angle. Suppose A = 60 deg, C = 90 deg and a and c are the corresponding sides. Then, by the sine rule a/c = sin(A)/sin(C) a/c = sin(60)/sin(90) = sqrt(3)/2
The ratios are "small to large".
The scale factor.
Area ratio = (edge-length ratio)2 Volume ratio = (edge-length ratio)3 Volume ratio = (area ratio)3/2
the ratios in such a triangle are 1:2:sqrt(3) so the longest length is opposite the 90 degree angle and is twice as large as the length opposite the 30 degree angle
The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.In terms of ratios, the sine of an angle is defined, in a right angled triangle, as the ratio of lengths of the opposite side to the hypotenuse.
The longer leg is opposite the 60 deg angle. Suppose A = 60 deg, C = 90 deg and a and c are the corresponding sides. Then, by the sine rule a/c = sin(A)/sin(C) a/c = sin(60)/sin(90) = sqrt(3)/2
Example: triangle, first one is 3:4:5 (length of sides), second is 9:12:15. Using length of similar lines, ie the longest, reveals the longer is three times the length, revealing the scale difference ie 3
There's no such thing as the "length of a 30-60-90". The ratios of the lengths of the legs of such a triangle to the length of the hypotenuse are 1/2 and 1/2(sqrt(3).
By themselves, they cannot. Two similar triangles have the same angels and so they have the same trig ratios. You need to know the length of at least one side to determine the area.
Restate the question: triangle QRS is similar to triangle DEF ..... (If this isn't your question, then change the wording and ask it again) Then (QR/DE) = (RS/EF) = (SQ/FD)
The ratios are "small to large".
The cosine function on a right triangle is Adjacent leg divided by the hypotenuse of the triangle.
The scale factor.
Area ratio = (edge-length ratio)2 Volume ratio = (edge-length ratio)3 Volume ratio = (area ratio)3/2
Using trigonometric ratios.