A parallelogram ABCD has lengths of sides and angles given below. Find the length of the diagonals AC and BD. (Round your answers to two decimal places.)
AB = DC = 6 and AD = BC = 5, angleA = 40°
See 4-13-11, 12:32am post for solution.
To find the length of the diagonals AC and BD in the parallelogram ABCD, we can use the properties of parallelograms.
Step 1: Determine the other angles of the parallelogram.
Since opposite angles in a parallelogram are congruent, angle B is also 40°.
Step 2: Use the given lengths and angles to apply the Law of Cosines.
Use the Law of Cosines to find the lengths of the diagonals AC and BD.
For diagonal AC, we can use triangle ABC:
AC^2 = AB^2 + BC^2 - 2 * AB * AC * cos(angle B)
Substituting the given values into the equation:
AC^2 = 6^2 + 5^2 - 2 * 6 * AC * cos(40°)
For diagonal BD, we can use triangle ABD:
BD^2 = AB^2 + AD^2 - 2 * AB * AD * cos(angle A)
Substituting the given values into the equation:
BD^2 = 6^2 + 5^2 - 2 * 6 * BD * cos(40°)
Step 3: Solve for the diagonals AC and BD.
To find the lengths of the diagonals, we need to solve the equations for AC^2 and BD^2. Then, we can take the square root to find the lengths.
Using a calculator, apply the calculations to find the values of AC and BD, rounded to two decimal places.