Question

If a rhombus has sides 8m and one diagonal is 12cm, find the angles of the rhombus.

Answer 1

The angles of the given rhombus are approximately 30.96° and 59.04°.

Step-by-step explanation:

A rhombus is a four-sided polygon with opposite sides that are parallel and congruent. In a rhombus, the opposite angles are equal. Let's find the angles of the given rhombus.

Given that the sides of the rhombus are 8m and one diagonal is 12cm, we can use the properties of a rhombus to find the angles.

Using the Pythagorean theorem, we can find the length of the other diagonal:

1. Let the length of the other diagonal be d.
2. Using the Pythagorean theorem, we have: 82 + d2 = 122.
3. Simplifying the equation, we get: 64 + d2 = 144.
4. Subtracting 64 from both sides, we get: d2 = 80.
5. Taking the square root of both sides, we find: d = √80 = 8√5.

Now that we know the length of both diagonals, we can find the angles using trigonometry. Let's call the acute angle formed by the diagonals θ.

Using sine and cosine ratios, we have:

1. Sine ratio: sin(θ) = (1/2) * (8√5 / 8) = √5/2.
2. Cosine ratio: cos(θ) = (1/2) * (12 / 8√5) = 3√5/10.

Therefore, the acute angles of the rhombus are approximately θ ≈ 30.96° and θ ≈ 59.04°.