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construct a quadrilateral LION, Where LI = 5cm, IO=6 cm, ON = 7cm, NL = 3cm and LO = 9cm


Sagot :

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

View image oeerivona
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