A rhombus has sides 10 cm long and an angle of 60 degrees. Find the distance between a pair of opposite sides.
can u plz post the answer down with explanation.
thanx, :)
BD=10 and AC=10√3
Hhs
To find the distance between a pair of opposite sides of a rhombus, we need to use the formula for the height of a rhombus.
In a rhombus, the height is the perpendicular distance between a pair of opposite sides. The formula for the height of a rhombus is given by:
h = a * sin(θ)
where 'h' is the height, 'a' is the length of one of the sides, and θ is the measure of one of the acute angles.
In this case, the length of one side of the rhombus is 10 cm, and the measure of one of the acute angles is 60 degrees.
Plugging in the values into the formula:
h = 10 cm * sin(60 degrees)
Calculating the value:
h = 10 cm * √(3)/2
h = 10√(3)/2 cm
Simplifying the expression:
h = 5√(3) cm
Therefore, the distance between a pair of opposite sides of the rhombus is 5√(3) cm.
since all the sides are equal, the altitude is
10 sin60° = 5√3
To see this, draw the rhombus ABCD and drop an altitude from D to AB. Now you have a right triangle with hypotenuse=10 and base angle=60°