3.13 Radial surveys

Consider the following triangle, taken from a field diagram. Note that all measurements are in metres.

Consider the following diagram of a field. Note that all measurements are in metres.

Consider the following field diagram. Note that all measurements are in metres.

Consider the following diagram. Note that all measurements are in metres.

Consider the following field diagram. Find the perimeter of the whole field correct to the nearest metre.

Consider the following diagram. Points A, B and C lie at true bearings of 328 \degree, 110 \degree and 196 \degree respectively from point X.

Note that all measurements are in metres.

Consider the following field diagram. Points A, B and C lie at true bearings of 75 \degree, 166 \degree and 302 \degree respectively from point X. Note that all measurements are in metres.

Find the perimeter of the field diagram, correct to two decimal places.

Consider the following radial survey of a block of land. In the survey, B is directly east of A.

Consider the following field diagram. Note that all measurements are in metres.

In the field diagram below, A_1 = 275.23 \text{ m}^2, A_2 = 170.63\text{ m}^2and A_3 = 416.90 \text{ m}^2. Find the area of the whole field correct to two decimal places.

Consider the following diagram. Points A, B and C lie at true bearings of 309 \degree, 52 \degree and 182 \degree respectively from point X, where AX = 20, BX = 32 and CX = 26. Note that all measurements are in metres.

Consider the following four sided field diagram. The four lines passing from the centre to the corners of the field are at true bearings of 46 \degree, 111 \degree, 233 \degree and 311 \degree. Note that all measurements are in metres.

Find the area of the field correct to two decimal places.