In a rhombus PQRS,the diagonals intersect at O.given that angle=120 degree and OP=3 cm.what is the side of the rhombus.
To find the length of the side of the rhombus, we can use the properties of a rhombus.
In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they intersect at a right angle, and they divide each other into two equal halves.
First, let's find the length of the other diagonal, OR. Since the diagonals of a rhombus are equal in length, we know that OR is also 3 cm.
Now, we can use the properties of a right triangle to find the length of PR, which is one of the sides of the rhombus.
In triangle OPR, we have a right angle at O, and we also know that angle POR is 120 degrees. Therefore, angle PRO is (180 - 90 - 120) = 30 degrees.
We can use trigonometric ratios to find the length of PR. Since we have the opposite (OP) and adjacent (OR) sides with respect to angle PRO, we can use the tangent function.
Tangent(PRO) = Opposite(OP) / Adjacent(OR)
Tan(30 degrees) = PR / 3 cm
Since the tangent of 30 degrees is 0.5774 (approximately), we can solve for PR:
0.5774 = PR / 3 cm
Cross-multiplying:
PR = 3 cm * 0.5774
PR ≈ 1.7322 cm
Therefore, the side length of the rhombus is approximately 1.7322 cm.
What angle = 120 ?
If you mean angle PQR for example
then
triangle PQO is a 30 60 90 triangle
the cos 30 = 3/side
side = 3/cos 30