Question

Find the amount of fencing needed to enclose the triangular piece of land? <A = 48 degrees <B = 56 degrees Side b(opposite of angle B) = 300 meters

Answer 1

Amount of fencing needed `color(maroon)( = 916.77 m`

Explanation:

We need to find the perimeter of the triangle for fencing.

`hat A = 48^@, hat B = 56^@, hat C = 180 - 48 - 56 = 76^@, b = 300 m`

Applying Law of Sines,

`a / sin A = b / sin B = c / sin C`

`a = (300 * sin 48) / sin 56 = 268.92 m`

`c = (300 * sin (74)) / sin 56 = 347.85 m`

Perimeter of `Delta = 300 + 268.92 + 347.85 = color (maroon)(916.77 m`

Answer 2

Amount of fencing needed to enclose the land is `920.04` meter.

Explanation:

Angle between Sides `b and c` is `/_A = 48^0`

Angle between Sides `a and c` is `/_B = 56^0 :.`

Angle between Sides `a and b` is `/_C= 180-(48+56)=76^0`

The sine rule states if `a, b and c` are the lengths of the sides

and opposite angles are `/_A, /_B and /_C` in a triangle, then:

`a/sin A = b/sin B=c/sin C ; b=300 :. b/sin B=c/sin C` or

`300/sin 56=c/sin 76 or c = (300 * sin 76)/sin 56~~ 351.12` m

Similarly, `b/sin B=a/sin A or 300/sin 56=a/sin 48` or

`a = (300 * sin 48)/sin 56~~268.92` m.

Perimeter of the triangular piece of land is

`= (a+b+c)= 268.92+300+351.12 = 920.04` meter

Amount of fencing needed to enclose the land is `920.04` meter [Ans]