The height BM drawn from the vertex ABCD makes an angle of 30 AM with the side AB and is equal to 5 cm.

The height BM drawn from the vertex ABCD makes an angle of 30 AM with the side AB and is equal to 5 cm. Find the length of the dioganal BD of the rhombus if the point M lies on the side AD.

So BM is the height, then the angle BMA is straight, therefore the triangle ABM is right-angled, then:

| AB | = | AM | / sin (ABM) = 5 / sin (30) = 5: 1/2 = 10 cm.

The BAM angle is:

BAM = 180 – 90 – 30 = 60 degrees.

Then the diagonal | BD | is equal to:

| BD | = 2 * | AB | * sin (BAM / 2) = 2 * 10 * sin (60/2) = 10 cm.