Thank you for visiting The diagonals of a parallelogram are 26 5 meters and 39 4 meters If they meet at an angle of 137 5 find the length. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer:
13.4m
Step-by-step explanation:
Please find the attached.
Thank you for reading the article The diagonals of a parallelogram are 26 5 meters and 39 4 meters If they meet at an angle of 137 5 find the length. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
Answer:
13.4 m
Step-by-step explanation:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.
The diagonals of a parallelogram bisect each other and form two pairs of congruent triangles. Each triangle has side lengths that are half the length of each diagonal. Given that the diagonals of the parallelogram are 26.5 meters and 39.4 meters, the corresponding side lengths of each triangle are 13.25 meters and 19.7 meters.
When the diagonals bisect each other, they form two pairs of vertically opposite angles at their intersection. These angles are the apex angles of each pair of congruent triangles. Given that the diagonals intersect at an angle of 137.5°, the apex angle for one pair of congruent triangles is 137.5°, while the apex angle for the other pair is 180° - 137.5° = 42.5°.
The unknown sides of the pair of congruent triangles with an apex angle of 137.5° will be the longer sides of the parallelogram. The unknown sides of the pair of congruent triangles with an apex angle of 42.5° will be the shorter sides of the parallelogram.
Since we have the lengths of two sides and the included angle, we can use the Law of Cosines to find the length of the side opposite the angle.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Law of Cosines}}\\\\c^2=a^2+b^2-2ab \cos C\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a, b$ and $c$ are the sides.}\\\phantom{ww}\bullet\;\textsf{$C$ is the angle opposite side $c$.}\end{array}}[/tex]
In this case:
- a = 13.25 m
- b = 19.7 m
- c = shorter side length of parallelogram
- C = 42.5°
Substitute the values into the equation and solve for c.
[tex]c^2=13.25^2+19.7^2-2(13.25)(19.7)\cos 42.5^{\circ} \\\\ c^2=175.5625+388.09-522.05\cos 42.5^{\circ} \\\\ c^2=563.6525-522.05\cos 42.5^{\circ} \\\\ c=\sqrt{563.6525-522.05\cos 42.5^{\circ}} \\\\ c=13.369998740... \\\\c=13.4\; \sf (1\;d.p.)[/tex]
Therefore, the length of the shorter side of the parallelogram rounded to one decimal place is:
[tex]\LARGE\boxed{\boxed{\sf 13.4\; m}}[/tex]
