The diagram below shows a triangle ABC.
(a) Calculate the length, in cm, of AC.
(b) A quadrilateral ABCD is now formed so that AC is a diagonal, ÐACD = 45° and
AD = 14 cm. Calculate the two possible values of ÐADC.
(c) By using the acute ÐADC from (b), calculate
(i) the length, in cm, of CD,
(ii) the area, in cm2, of the quadrilateral ABCD
Using cosine rule,
AC2 = AB2 + BC2 – 2 (AB)(BC) ÐABC
AC2 = 162 + 122 – 2 (16)(12) cos 70o
AC2 = 400 – 131.33
AC2 = 268.67
AC = 16.39 cm