Answer:
Part A) BD = 6.5 cm
Part B) see explanation
Step-by-step explanation:
See the attached figure
Part A) Find the length of BD
ΔDAB is a right triangle at A, AB is 3.3cm , DA is 5.6cm
So, DB is the hypotenuse
Using Pythagorean equation:
DB = √(AD² + AB²) = √(3.3² + 5.6²) = √42.25 = 6.5 cm
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Part B) Show that angle BCD is 90°
Given: CD is 5.2cm , BC is 3.9cm and DB = 6.5 cm
So, CD² = 5.2² = 27.04
BC² = 3.9² = 15.21
DB² = 6.5² = 42.25
So, CD² + BC² = 27.04 + 15.21 = 42.25 = DB²
So, DB represent a hypotenuse at ΔBCD
So, the apposite angle of BD is a right angle
So, ∠BCD = 90°
