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Rampur Sarpanch requested one of his villager to donate a 6m wide land adjusted to his 132.8m long side of his right triangular plot outside the village . The other sides of the plot is 123m and 50m .On his donated land , the Sarpanch wants to construct a link road which provides the connectivity with the other villages and towns . The villager agreed at once . i) Find the area of the triangular plot remaining with the villager .

Respuesta :

Answer:

The answer is 3030.72 m³

Step-by-step explanation:

Please refer to attached file for graphical representation.

Formulas used:

Area = (a*b)/2

Trigonometry: Tan (t) = opposite/adjacent

Assume:

Villager plot has 3 sides: hypotenuse=C, adjacent=A, opposite=B

Plot given has 3 sides: hypotenuse=z, adjacent=y, opposite=x

Angle common between them is t.

Step 1:

For t:

Tan (t) = a/b

Tan (t) = 123/50

Tan (t) = 2.46

Step 2:

For y:

Tan (t) = y/x

2.46 = y/6

y = 2.46*6

y = 14.76

Step 3:

Villagers old plot area: B = (a*b)/2 = (123*50)/2

B = 3075 m³

Step 4:

Plot donated area: C = (x*y)/2 = (6*14.76)/2

C = 44.28 m³

Step 5:

Villager remaining plot:

A = B-C

A= 3075-44.28

A = 3030.72 m³

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