Applying the tangent ratio, the size of ∠CDA in the given trapezium, to 1 decimal place is: 27.6°.
What is Tangent Ratio?
Given a right triangle, the tangent ratio is a Trigonometric ratio which is expressed as: tan ∅ = opposite side / adjacent side.
First, find AE using the Pythagorean Theorem:
AE = √(6.5² - 6²)
AE = 2.5 cm
Find FD:
FD = AE + BC
FD = 2.5 + 9 = 11.5
Using the tangent ratio, find m∠CDA:
∅ = ∠CDA
opposite = FC = 6 cm
adjacent = FD = 11.5
Therefore:
tan ∠CDA = 6/11.5
∠CDA = tan^(-1)(6/11.5) = 27.55 ≈ 27.6°
Therefore, applying the tangent ratio, the size of ∠CDA in the given trapezium, to 1 decimal place is: 27.6°.
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