A rhombus has diagonals of lenth 12 cm and 7 cm respectively. Find the larger angle of the rhombus
Answer to the question
The diagonals are perpendicular, and they bisect each other. So, you have 4 right triangles with legs 6 and 3.5
The diagonals bisect the vertex angles, so the angle is
2arctan(6/3.5)
Why did the rhombus go to the gym? To work on its angles, of course! Now, let's solve your problem. In a rhombus, any two opposite angles are congruent. So, we just need to find one angle in order to find the larger angle of the rhombus.
Using the diagonals, we can divide the rhombus into four congruent right triangles. Let's focus on one of these triangles.
The larger diagonal divides the triangle into two congruent right triangles, each with sides measuring 6 cm, 7 cm, and the hypotenuse measuring 12 cm.
Now, we can use the Pythagorean Theorem: a² + b² = c². Plugging in the values, we have 6² + 7² = 12². Simplifying this equation gives us 36 + 49 = 144.
Combining like terms further, we have 85 = 144. Oh, that can't be right! Did I just solve a math problem or invent a new equation? Let me try again.
Using the same triangle, we can find the larger angle using the inverse tangent function (tan⁻¹) of the ratio of the opposite (7 cm) to the adjacent (6 cm) side.
So, tan⁻¹(7/6) ≈ 48.19°.
Therefore, the larger angle of the rhombus is approximately 48.19 degrees. I hope this answer tickles your funny bone!
To find the larger angle of a rhombus, we can use the properties of diagonals.
In a rhombus, the diagonals bisect each other at right angles. This means that the diagonals divide the rhombus into four congruent right triangles.
Let's label the length of one half of the larger diagonal as 'a' and the length of one half of the smaller diagonal as 'b'.
Given that the length of the larger diagonal is 12 cm, we have a = 12/2 = 6 cm.
And given that the length of the smaller diagonal is 7 cm, we have b = 7/2 = 3.5 cm.
The larger angle of the rhombus can be found using trigonometry. We can use the properties of the right triangle formed by one half of the larger diagonal, one half of the smaller diagonal, and one side of the rhombus.
Let's label the larger angle of the rhombus as θ.
Using the tangent function, we can write:
tan(θ) = (a / b)
Plugging in the values we found:
tan(θ) = (6 / 3.5)
Now, we can find the angle θ by taking the inverse tangent (arctan) of both sides:
θ = arctan(6 / 3.5)
Using a calculator, we find:
θ ≈ 60.26 degrees
Therefore, the larger angle of the rhombus is approximately 60.26 degrees.
To find the larger angle of a rhombus, we need to apply the properties of a rhombus. In a rhombus, the diagonals bisect each other at right angles. This means that the larger angle of the rhombus is formed by one-half of the longer diagonal.
First, let's determine which diagonal is longer. The given lengths of the diagonals are 12 cm and 7 cm. Since the longer diagonal is usually not specified, let's assume that the 12 cm diagonal is the longer one.
Next, we divide the length of the longer diagonal by 2 to find one-half of its length:
12 cm ÷ 2 = 6 cm
Therefore, one-half of the longer diagonal has a length of 6 cm. This is also the length of the side of the rhombus.
Now, we can find the larger angle using trigonometry. Since we have the lengths of the two sides of a right-angled triangle (6 cm and 7 cm), we can use the inverse tangent (arctan) function to find the angle:
tan^-1(6 cm/7 cm) ≈ 38.66 degrees
Therefore, the larger angle of the rhombus is approximately 38.66 degrees.