Favorite Answer. Diagonals and other side 3. It is done with the help of law of cosines. This calculator computes the diagonals of a parallelogram and adjancent angles from side lengths and angle between sides. I have a parallelogram here. You could use the law of cosines. The sides measure 4.13" cm." I can't use the law of cosines, because it only applies to the longer diagonal. I have been racking my brain for hours here. and 15.35" cm.". According to the cosine theorem, the side of the triangle to the second degree is equal to the sum of the squares of its two other sides and their double product by the cosine of the angle between them. You can use the calculator for each formula. Since any diagonal of a parallelogram divides it into two congruent triangles, you can calculate the diagonal by knowing the sides of the parallelogram and the angle between them. The diagonals of a parallelogram bisect each other. By using this website, you agree to our Cookie Policy. A = 32(41)sin(a) = 656 --> sin(a) = .5 --> a = 150 degrees Check the picture. The only answer choice in the range of 24–39 cm is choice B. 8 years ago. We will approach this problem by a different approach. Diagonals of a Parallelogram. You know the angle that shares either side with the 60 degree angle must be supplementary. Thanks so much :D. Answer Save. Inside Any Quadrilateral . You get the equation = . Free Parallelogram Sides & Angles Calculator - Calculate sides, angles of an parallelogram step-by-step This website uses cookies to ensure you get the best experience. Answer to Find the length of the longer diagonal of this parallelogram. _____ You are given sufficient information to use the Law of Cosines to find the diagonal length. a = side a lengths b = side b lengths (base) p = shorter diagonal length q = longer diagonal length Solution Let x be the length of the second diagonal of the parallelogram. Relevance. Diagonals and angle between them 2. ft. And there is a parallelogram in any quadrilateral. Find the length of the second diagonal of the parallelogram. In other words the diagonals intersect each other at the half-way point. Angle and height. If we call it "c", then the angle opposite that diagonal is the larger of the angles in the parallelogram: 120°. We know the length of BD and of AC. В. Josh K. Lv 6. This can be accomplished by looking at the area of the parallelogram. Parallelogram Shape. We know, by the properties of the parallelogram, that diagonals are cut into two equal parts at the point of intersection. First find the obtuse angle included between two sides of the parallelogram. 3 Answers. Apply the formula from the Theorem. The longer diagonal is longer than either side, but shorter than their sum. Using only the shorter side length of 12 centimeters, the longer side length of 15 centimeters, and the obtuse angle between them of 118 degrees, find the length of the shorter diagonal. •C С 4 ft. 30° 1049 A D [ ? ] The Perimeter is 2 times the (base + side length): Perimeter = 2(b+s) ... (12 cm + 6 cm) = 2 × 18 cm = 36 cm. In a parallelogram, the sides are 8 cm and 6 cm long. One diagonal is 5 cm long. Find the longer diagonal of a parallelogram having sides of lengths 10 and 15 and an angle measure 60 degrees? However, we don't have an angle that is on the exterior (ex BDC, BCD or DBC), so we don't have enough information to use Cosine's Law. Then use the law of cosines to find the unknown length of the longer diagonal. First, we use law of cosines to find out d1, then we find second angle of parallelogram, which is , then we again use law of cosines to find out d2. Length of a side of a parallelogram if you know: 1.