a sign is in the shape of rhombus with a 60 degree angle and sides of 9cm long. Find its are to nearest tenth?
The height is 9*sin60 = 7.79
area = 9*7.79 = 70.15 or 7.2
To find the area of a rhombus, you need to know the length of the diagonals. However, in this case, the length of the diagonals is not given. Instead, we have the angle and the length of the sides.
To find the area of the rhombus, you can use the following formula:
Area = (product of the diagonals) / 2
Since we don't know the diagonals, we need to find them using the given information.
In a rhombus, opposite angles are equal. Therefore, since one angle is 60 degrees, the opposite angle is also 60 degrees.
To find the length of the diagonals, we can use the law of cosines.
Let's label the rhombus as ABCD, with the side length of 9 cm. The diagonals can be labeled as AC and BD.
1. Using the law of cosines, we can find the length of AC:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(angle ABC)
AC^2 = 9^2 + 9^2 - 2 * 9 * 9 * cos(60 degrees)
AC^2 = 81 + 81 - 162 * 0.5
AC^2 = 162 - 81
AC^2 = 81
AC = √81
AC = 9 cm
2. Since opposite sides in a rhombus are equal, BD is also 9 cm.
Now we can calculate the area of the rhombus:
Area = (AC * BD) / 2
Area = (9 * 9) / 2
Area = 81 / 2
Area = 40.5 cm^2
Therefore, the area of the rhombus is 40.5 square cm (rounded to the nearest tenth).