Answer:
DE = 11.25 units
Step-by-step explanation:
The image of the quadilateral BCED and the extensions of BD and CE to move past B and C to meet at A is presented in the attached file to this answer.
Let the angle at A be θ
Let the length of DE be x
ABC forms a triangle which van allow θ to be obtained using cosine rule.
BC² = AB² + AC² - (2×AB×AC×cos θ)
BC = 9
AB = 24
AC = 28
9² = 24² + 28² - (2×24×28×cos θ)
-1279 = -1344 cos θ
Cos θ = (1279/1344) = 0.9516
θ = 17.89°
Note that ADE also forms a triangle and we can also use cosine rule to obtain the required side DE
DE² = AD² + AE² - (2×AD×AE×cos θ)
DE = ?
AD = AB + BD = 24 + 11 = 35
AE = AC + CE = 28 + 2 = 30
θ = 17.89°
DE² = 35² + 30² - (2×35×30×cos 17.89°)
DE² = 126.54
DE = √126.54 = 11.25
Hope this Helps!!!
The value of DE in the quadrilateral is 11.25 units.
From the information given, the cosine rule can be used. This will be:
BC² = AB² + AC² - (2 × AB ×AC × cos)
Therefore,
9² = 24² + 28² - (2 × 24 × 28 × cos)
cos = 17.89°
Therefore, the value of DE will be calculated thus:
DE² = 35² + 30² - (2 × 35 × 30 × cos 17.89)
DE = ✓126.54
DE = 11.25
In conclusion, the value of DE is 11.25 units.
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