a. To compute the coordinates of the property corners A, B, C, D, and E, we can use the
method of traversing. Starting from the known coordinates of station K (1000 N, 1000 E)
and moving in the specified directions with the given distances, we can calculate the
coordinates of the property corners as follows:
Let's denote the coordinates of the property corners as:
- A: (N_A, E_A)
- B: (N_B, E_B)
- C: (N_C, E_C)
- D: (N_D, E_D)
- E: (N_E, E_E)
Using the azimuth angles and distances provided:
1. For corner A:
Starting from K, moving in direction KA with a distance of 100.00 ft:
∘
NA = 1000 + 100 × sin(0 ) = 1100
∘
EA = 1000 + 100 × cos(0 ) = 1100
2. For corner B:
Starting from K, moving in direction KB with a distance of 165.34 ft:
∘
′
′′
∘
′
′′
NB = NA + 165.34 × sin(87 35 28 )
EB = EA + 165.34 × cos(87 35 28 )
3. For corner C:
Starting from K, moving in direction KC with a distance of 172.05 ft:
∘
′
′′
∘
′
′′
NC = NB + 172.05 × sin(125 32 15 )
EC = EB + 172.05 × cos(125 32 15 )
4. For corner D:
Starting from K, moving in direction KD with a distance of 138.29 ft:
∘
′
′′
∘
′
′′
ND = NC + 138.29 × sin(167 28 16 )
ED = EC + 138.29 × cos(167 28 16 )
5. For corner E:
Starting from K, moving in direction KE with a distance of 82.46 ft:
∘
′
′′
∘
′
′′
NE = ND + 82.46 × sin(284 02 10 )
EE = ED + 82.46 × cos(284 02 10 )
b. To compute the area of the property, we can use the coordinates of the property corners
to determine the shape of the lot and then calculate the area using the coordinates of the
corners.
c. To compute the bearings and distances of the five sides of the property, we can use the
coordinates of adjacent property corners to determine the azimuth angles and distances of
each side.
d. To find the coordinates of points MNOP representing the corners of the house
foundation, we can use the given dimensions (50 ft wide and 40 ft deep) to determine the
coordinates based on the orientation relative to side AE and the center at point K.