# A garden has a triangle shape with two of the angles measuring 22 degrees and 98 degrees, respectively. If the side opposite the 22-degree angle measures 120 ft, how many ft of fence material would be needed to enclose the garden?

1
by SixSeven

• Brainly User
2016-07-08T14:01:34+08:00
Find the measure of each side to solve for the perimeter of the triangle.

Given:
a = 120 ft              b = ?                  c = ?
A = 22°                 B = 98°              C= 180-(22 + 98) ⇒ 180 - 120 = 60°

Use Law of Sines to find the measurement of two other sides:
1)  Solve for b:

a              b
---------- = -------------
Sin A          Sine B

120 ft                b
-------------- =  ----------------
Sin(22°)          Sin (98°)

120 ft (Sin 98°)           120 ft (0.990)        118.8 ft
b  = --------------------   =   --------------------- = ------------  =  317 ft
Sin 22°                        0.375                0.375

2) Solve for c:

a                    c
-------------- = ----------------
Sin A               Sin C

120 ft              c
------------- = -------------
Sin 22°          Sin 60°

120 ft (Sin 60°)      120 ft (0.866)        103.92 ft
c = --------------------  =   ------------------ =   --------------  =  277 ft
0.375                       0.375                  0.375

The sides of the triangles are:

a = 120 ft.      b = 317 ft     c = 277 ft.

Perimeter of the triangular garden = a + b + c

120 ft. + 317 ft + 277 ft = 714 ft.

ANSWER:  714 ft. of fence materials would be needed to enclose the garden.