A SIDE AND A DIAGONAL OF A PARALELOGRAM ARE 12 INCHES AND 19 INCHES RESPECTIVELY. THE ANGLE BETWEEN THE DIAGONALS, OPPOSITE THE GIVEN SIDE IS 124 DEGREES. FIND THE LENGTH OF THE OTHER DIAGONAL
To find the length of the other diagonal of the parallelogram, we can use the law of cosines.
Let's call the given side of the parallelogram "a" and the given diagonal "b". The angle between the diagonals, opposite the given side, is 124 degrees.
Using the law of cosines, we have:
c^2 = a^2 + b^2 - 2ab*cos(C)
Where c is the length of the other diagonal of the parallelogram, and C is the angle between the diagonals.
Substituting the given values into the formula:
c^2 = 12^2 + 19^2 - 2 * 12 * 19 * cos(124 degrees)
Now we can calculate the length of the other diagonal.
c^2 = 144 + 361 - 2 * 12 * 19 * cos(124 degrees)
Using the trigonometric identity cos(180 - θ) = -cos(θ), we can simplify the equation:
c^2 = 144 + 361 + 2 * 12 * 19 * cos(56 degrees)
c^2 = 505 + 456 * cos(56 degrees)
Now we can use a calculator to find the value of cos(56 degrees), multiply it by 456, and then add it to 505. Finally, take the square root of the result to find the length of the other diagonal, c.