In quadrilateral ABCD, ∠ABD = ∠BCD = 90°. ∠DAB = 48°, ∠ADC = 106° and BC = 7 cm. Calculate the length, in cm to 3 significant figures, of (a) BD, (b) BA

Answer 1

We have two triangles: BAD and BCD.

In triangle BAD, since <DAB = 48 and <ABD = 90, < BDA = 42.

Since < ADC = 106 and < BDA = 42, < BDC = their difference = 64.

In triangle BCD, Sine <BDC = BC/BD => sine 64 = 7/ BD

In triangle BAD, sine 42 = BA/BD.