The shorter diagonal of a rhombus is 10 inches long, and the angle the
diagonal forms with the side measures 60º. Find the area of the
rhombus.
I really don't know where to start. I know that the area formula for a
rhombus is
A=1/2*d1*d2
So if I know that one of the D is 10, how do i get the area? I don't know
where the angle measurement is very helpful either.
Help?
Draw the picture.
The angle helps a lot. You know the diagonal bisects that corner angle, so now you know the corner angles. If you know the corner angles, you know the central angles. With these, you can determine the lengths of all parts of the figure.
Repost if you need more help.
Isn't the central angle 90 because the diagonals intersect? How do I find the 2nd diagonal?
wow i was 1 when this was posted
I apologize for the confusion in my previous response. Let's clarify the situation with the given information.
In a rhombus, the diagonals intersect at right angles, so the central angle is indeed 90 degrees, not 60 degrees as originally mentioned. This means that the angle formed by the diagonal and one side (not the corner angle) is actually 30 degrees (90 degrees minus 60 degrees).
To find the length of the second diagonal, we can use the properties of a rhombus. In a rhombus, the diagonals bisect each other and are perpendicular. This means that each diagonal divides the rhombus into two congruent right triangles.
In one of these right triangles, we have the following information:
- One leg is half of the shorter diagonal, which is 10 inches / 2 = 5 inches.
- The angle opposite this leg is 30 degrees.
Now we can use trigonometric functions to find the length of the other leg of the right triangle, which is equal to half of the longer diagonal (let's call it d2). In this case, we can use the sine function:
sin(30 degrees) = (opposite side) / (hypotenuse)
sin(30 degrees) = (5 inches) / (d2/2)
Using the value of sin(30 degrees) = 1/2, we can solve for d2:
1/2 = 5 inches / (d2/2)
1 = 5 inches / (d2/2)
1 = 10 inches / d2
d2 = 10 inches
So, we have found that the length of the second diagonal (d2) is also 10 inches.
Now that we know both diagonals (d1 = 10 inches and d2 = 10 inches), we can substitute them into the formula for the area of a rhombus:
A = (1/2) * d1 * d2
A = (1/2) * 10 inches * 10 inches
A = 50 square inches
Therefore, the area of the rhombus is 50 square inches.
I apologize for the mistake in my previous response and any confusion caused.