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°.
(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.
This looks suspiciously like the PQRS ranch.
Where do you get stuck? Remember the law of cosines and the law of sines.
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 = ?
(a) To draw the diagram, follow these steps:
1. Start by drawing a line segment to represent the distance between A and B, which is 8 cm (since the scale is 1 cm to 1 km).
2. From the endpoint of line AB, draw a line segment at an angle of 30° to represent BC. The length of BC would be 6 cm according to the scale.
3. From the endpoint of line BC, draw a line segment at an angle of 300° to represent CD. The length of CD would be 7 cm according to the scale.
4. Finally, label the points A, B, C, and D accordingly on the diagram.
(b) Using the scale drawing:
(i) To determine the bearing of A from D, follow these steps:
1. Draw a line segment from point D to point A.
2. Measure the angle formed by the line segment AD with respect to the horizontal line (east-west direction) using a protractor.
3. The measured angle represents the bearing of A from D.
(ii) To determine the distance BD in kilometers using the scale drawing, follow these steps:
1. Measure the length of line segment BD on the diagram in centimeters.
2. Convert the measured length from centimeters to kilometers using the scale. In this case, since the scale is 1 cm to 1 km, the measured length in centimeters would directly represent the distance in kilometers.