https://r2.erweima.ai/mathbot/image/1725926282262mvsv65tq.jpg

The problem involves a parallelogram with sides of 30 cm and 70 cm and an angle of 65° between them. It asks if the length of diagonal \( AC \) is approximately 87 cm.

To check if this is true, we can use the law of cosines for the diagonal:

\[
AC^2 = AB^2 + AD^2 - 2 \cdot AB \cdot AD \cdot \cos(\theta)
\]

Where:
- \( AB = 30 \) cm
- \( AD = 70 \) cm
- \( \theta = 65^\circ \)

Let me calculate the value of \( AC \).The calculated length of diagonal \( AC \) using the law of cosines is approximately 63.44 cm, not 87 cm. Therefore, the statement that the diagonal \( AC \) is 87 cm is **false**.

Would you like further details or have any questions? Here are five related questions:

1. How would you calculate the length of the other diagonal in the parallelogram?
2. What other properties of a parallelogram can be determined using side lengths and angles?
3. Can you apply the law of cosines to other types of polygons, such as triangles or trapezoids?
4. What happens to the diagonals of a parallelogram when the angles are changed?
5. How does the area of the parallelogram relate to its side lengths and angles?

**Tip:** In any non-right triangle or parallelogram, the law of cosines is a powerful tool to find unknown side lengths when angles are involved.

Un paralelogramo tiene lados de longitudes de 30 cm y 70 cm y un ángulo de 65°. La longitud de la diagonal AC= 87 cm (aproximadamente).

Learn how to verify if the diagonal of a parallelogram with sides of 30 cm and 70 cm, and an angle of 65°, is approximately 87 cm. This problem uses the law of cosines to determine the diagonal's true length. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation