Final answer:
To approximate the lengths of the diagonals of a rhombus, we can use the properties of the rhombus. By considering one of the triangles formed by the diagonals, we can use the law of cosines to find the lengths of the diagonals. The approximate lengths of the diagonals to the nearest tenth of a centimeter are 162.5 cm.
Step-by-step explanation:
A rhombus is a quadrilateral with all sides of equal length. To approximate the lengths of the diagonals of a rhombus, we can use the properties of the rhombus.
Since the rhombus has all sides of length 100 cm, all angles are congruent. Therefore, the angle at the vertex is also 70°.
We can use the law of cosines to find the lengths of the diagonals. Let's denote the length of the diagonal as d.
By considering one of the triangles formed by the diagonals, we have:
d^2 = 100^2 + 100^2 - 2 * 100 * 100 * cos(70°)
By solving this equation, we find d ≈ 162.5 cm. Therefore, the approximate lengths of the diagonals to the nearest tenth of a centimeter are 162.5 cm.