To determine the lengths of sides AB and BC, let's first determine the missing angle, ∠ADC. Since the interior angles of a quadrilateral sum up to 360°, we have:
∠ADC = 360° - (∠DAB + ∠ABC + ∠BCD) = 360° - (90° + 115° + 90°) = 65°
Now, we can apply the law of sines on triangle ACD to find the length of side AC:
sin(∠ADC) / AC = sin(∠DAC) / CD
sin(65°) / AC = sin(90°) / 0.30
From this, we can solve for AC:
AC = 0.30 * sin(65°) / sin(90°) ≈ 0.2771 m
With the length of side AC, we can apply the law of cosines to triangle ABC to find the length of side AB:
AB^2 = AC^2 + BC^2 - 2(AC)(BC)cos(∠ABC)
AB = sqrt(AC^2 + BC^2 - 2(AC)(BC)cos(115°))
AB ≈ 0.4993 m
Now, to find the length of side BC, we will apply the law of cosines to triangle BCD:
BC^2 = CD^2 + BD^2 - 2(CD)(BD)cos(90°)
BC^2 = 0.30^2 + BD^2 (since cos(90°) = 0)
Since BD = AB - AD = 0.4993m - 0.25m = 0.2493m, we can find BC:
BC^2 = 0.30^2 + 0.2493^2
BC ≈ 0.3913 m
So, the lengths of sides AB and BC are approximately 0.4993m and 0.3913m, respectively.
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