Answer:
Area of the remaining triangle with the villager is 1243.13 m²
Step-by-step explanation:
Triangle ABC is the triangular plot of a villager shown in the figure attached.
Sarpanch requested the villager to donate land which is 6 m wide and along the side AC which measures 132.8m.
Other sides of the plot has been given as AB = 50m and BC = 123 m.
Now area of this land before donation =
=
= 3075 square meter
After donation of the land the triangle formed is ΔDBE.
In ΔABC,
tan(∠ABC) =
= 0.4065
∠ABC =
= 22.12°
In ΔEFC,
tanC =
0.4065 =
CF =
CF = 14.76 m
Since DE = AC - (CF + AG)
= 132.8 - (2×14.76)
= 132.8 - 29.52
= 102.48 m
Now in ΔDBE,
sin(∠DEB) =
sin(22.12) =
DB = 102.48×0.3765
= 38.59 m
Similarly, cos(22.12) =
0.9264 =
BE = 102.48×0.9264
= 94.94m
Now area of ΔDBE =
=
= 1831.87 square meter
Area of remaining triangle with the villager = Area of ΔABC - Area of ΔDBE
= 3075 - 1831.87
= 1243.13 square meter
