Final answer:
To find the lengths of the diagonals of a parallelogram with sides of lengths 8 and 7, and one angle of 40°, we can use the cosine rule to calculate the length of AC and BD.
Step-by-step explanation:
To find the lengths of the diagonals of a parallelogram with sides of lengths 8 and 7, and one angle of 40°, we can use the cosine rule. Let's call the diagonals AC and BD. Since the diagonals of a parallelogram bisect each other, we can divide the parallelogram into four congruent triangles. Applying the cosine rule to one of these triangles, we can find the length of the diagonal AC. Applying the cosine rule to another triangle, we can find the length of the diagonal BD.
Using the cosine rule:
AC^2 = (AB^2) + (BC^2) - 2(AB)(BC)cos(angle ABC)
Substituting the given values:
(AC^2) = (8^2) + (7^2) - 2(8)(7)cos(40°)
Simplifying and taking the square root, we get AC ≈ 11.39 units. Similarly, we can find the length of the diagonal BD as well.
Learn more about Parallelogram diagonals