The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.

Question

(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D.

(b) Use the scale drawing to determine:
(i) The bearing of A from D;
(ii) The distance BD in kilometers.

Answer 1

This looks suspiciously like the PQRS ranch.
Where do you get stuck? Remember the law of cosines and the law of sines.

Answer 2

AD = AB+BC+CD.
DA = -AD.

All angles are measured CW from +y-axis.
(I). AD = 8km[90o] + 6km[30o] + 7km[300o].
AD = (8*sin90+6*sin30+7*sin300) + (8*Cos90+6*Cos30+7*Cos300)I,
AD = 4.94 + 8.7i = 10km[30o].
DA = -AD = 10[30+180] = 10km[210o].

(ii). BD = BC + CD.
BD = 6km[30o] + 7km]300o].
BD = ?