The quadrilateral LION can be constructed on a computer or manually.
Description of construction using a computer;
Quadrilateral LION can also be constructed on a computer by constructing
∠LIO and ∠LNO, which are the two halves of quadrilateral LION, and rotate the two halves to fit as a single quadrilateral.
- Please find attached the drawing of the quadrilateral LION constructed using MS Word, with the angles ∠LIO and ∠LNO constructed using Rotation Options dialogue box.
Details of the Method by which the Quadrilateral LION is Constructed Manually
The lengths of the sides of the quadrilateral LION are;
LI = 5 cm
IO = 6 cm
ON = 7 cm
NL = 3 cm
Given that LI = 5cm, IO = 6 cm and LO = 9 cm, in ΔLIO, we have;
9² = 5² + 6² - 2×5×6×cos(∠LIO)
- ∠LIO = arccos(((5² + 6²) - 9²) ÷ (2×5×6)) ≈ 109.47°
Similarly;
- ∠LNO = arccos(((7² + 3²) - 9²) ÷ (2 × 7 × 3)) ≈ 123.2°
Angle of elevation, ∠LON, of NO from LO is therefore;
9 ÷ sin(123.2°) = 3 ÷ sin(∠LON)
- ∠LON = arcsine(3 ÷ (9 ÷ sin(123.2°) ≈ 16.2°
Using the above calculated angles, triangle ΔLIO can be constructed.
Construction of triangle ΔLNO
From point O, ∠LON ≈ 16.2° can be constructed using a protractor
The point N can be marked with a compass opened to 7 cm width with the compass placed at O and an arc drawn to intersect ON extended at N
The points N and L can joined to complete the construction of the quadrilateral LION.
Learn more about quadrilaterals here:
https://brainly.com/question/10634097
