Two sides of a parallelogram are 9 and 13 with an included angle of 57 degree & 29 minutes.fine the distance between the longer sides.
how about
sin 57°29' = h/9 ?
7.59
To find the distance between the longer sides of a parallelogram, we can use the sine rule. The formula for the sine rule is:
sin(A)/a = sin(B)/b = sin(C)/c,
where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the opposite sides of those respective angles.
In this case, we have the included angle between the shorter and longer sides of the parallelogram, which is 57 degrees and 29 minutes. Let's convert this angle to decimal degrees.
57 degrees and 29 minutes = 57 + (29/60) degrees
= 57.4833 degrees
We also have the lengths of the two sides of the parallelogram, which are 9 and 13.
Let's assume that the side adjacent to the given angle (57.4833 degrees) is 9 (a) and the side opposite to this angle is the distance we want to find (b).
Using the sine rule, we have:
sin(A)/a = sin(B)/b
Substituting the values we know:
sin(57.4833 degrees)/9 = sin(90 degrees)/b
sin(57.4833 degrees) = b/9
To isolate b, we can rearrange the equation:
b = 9 * sin(57.4833 degrees)
Using a scientific calculator, we find:
b ≈ 7.8547
Therefore, the distance between the longer sides of the parallelogram is approximately 7.8547 units.