To calculate the coordinates of points B and C, we use the formulas for coordinate geometry: $$E_X = E_A + D_{AX} \sin(\theta_{AX})$$ $$N_X = N_A + D_{AX} \cos(\theta_{AX})$$ where $(E_A, N_A)$ are the coordinates of point A, $D_{AX}$ is the distance from A to X, and $\theta_{AX}$ is the azimuth from A to X. Given: Point A coordinates: $(E_A, N_A) = (500 \text{ m E}, 550 \text{ m N})$ a) Calculate coordinates for point B: Distance $D_{AB} = 60 \text{ m}$ Azimuth $\theta_{AB} = 30^\circ 20' 20''$ Step 1: Convert the azimuth to decimal degrees. $\theta_{AB} = 30^\circ + \frac{20}{60}^\circ + \frac{20}{3600}^\circ = 30^\circ + 0.333333^\circ + 0.005556^\circ = 30.338889^\circ$ Step 2: Calculate the Easting coordinate for point B ($E_B$). $$E_B = E_A + D_{AB} \sin(\theta_{AB})$$ $$E_B = 500 \text{ m} + 60 \text{ m} \times \sin(30.338889^\circ)$$ $$E_B = 500 \text{ m} + 60 \text{ m} \times 0.505291$$ $$E_B = 500 \text{ m} + 30.31746 \text{ m}$$ $$E_B = 530.317 \text{ m}$$ Step 3: Calculate the Northing coordinate for point B ($N_B$). $$N_B = N_A + D_{AB} \cos(\theta_{AB})$$ $$N_B = 550 \text{ m} + 60 \text{ m} \times \cos(30.338889^\circ)$$ $$N_B = 550 \text{ m} + 60 \text{ m} \times 0.863005$$ $$N_B = 550 \text{ m} + 51.78030 \text{ m}$$ $$N_B = 601.780 \text{ m}$$ The coordinates of point B are $\boxed{\text{(530.317 m E, 601.780 m N)}}$. b) Calculate coordinates for point C: Distance $D_{AC} = 90 \text{ m}$ Azimuth $\theta_{AC} = 200^\circ 33' 55''$ Step 1: Convert the azimuth to decimal degrees. $\theta_{AC} = 200^\circ + \frac{33}{60}^\circ + \frac{55}{3600}^\circ = 200^\circ + 0.55^\circ + 0.015278^\circ = 200.565278^\circ$ Step 2: Calculate the Easting coordinate for point C ($E_C$). $$E_C = E_A + D_{AC} \sin(\theta_{AC})$$ $$E_C = 500 \text{ m} + 90 \text{ m} \times \sin(200.565278^\circ)$$ $$E_C = 500 \text{ m} + 90 \text{ m} \times (-0.351307)$$ $$E_C = 500 \text{ m} - 31.61763 \text{ m}$$ $$E_C = 468.382 \text{ m}$$ Step 3: Calculate the Northing coordinate for point C ($N_C$). $$N_C = N_A + D_{AC} \cos(\theta_{AC})$$ $$N_C = 550 \text{ m} + 90 \text{ m} \times \cos(200.565278^\circ)$$ $$N_C = 550 \text{ m} + 90 \text{ m} \times (-0.936216)$$ $$N_C = 550 \text{ m} - 84.25944 \text{ m}$$ $$N_C = 465.741 \text{ m}$$ The coordinates of point C are $\boxed{\text{(468.382 m E, 465.741 m N)}}$. Send me the next one 📸