A parallelogram has sides of 15 and 24 feet and an angle of 40 degrees .Find the diagonals.
I used law of cosines and found 1 of the diagonals to be 15.79 feet but what is the other? or are they the same?
hint: consecutive angles are supplementary.
so use 140 degrees instead?
yep. The sides have the same lengths, no matter which angle they surround.
To find the diagonals of a parallelogram, we need to use the given sides and angle. Let's denote the sides of the parallelogram as a = 15 feet and b = 24 feet, and the angle between them as θ = 40 degrees.
In a parallelogram, the opposite sides are congruent, meaning they have the same length. Therefore, both diagonals of a parallelogram will have the same length.
To find the length of the diagonals, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite side c, the following relation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we are interested in finding the length of the diagonals. Let's assume one of the diagonals is d.
Applying the law of cosines to the triangle formed by one of the sides, the other side, and the diagonal, we have:
d^2 = a^2 + b^2 - 2ab * cos(θ)
Plugging in the values, we get:
d^2 = 15^2 + 24^2 - 2 * 15 * 24 * cos(40°)
Calculating this expression, we find:
d^2 ≈ 225 + 576 - 720 * cos(40°)
d^2 ≈ 801.5
Taking the square root of both sides, we obtain:
d ≈ √801.5
Using a calculator, we find that d ≈ 28.32 feet (rounded to two decimal places).
So, the length of both diagonals of the parallelogram is approximately 28.32 feet.