A horse corral is situated on a triangular plot of land. Two sides of the plot are 150 feet long and they meet at an angle of 55
°. A fence is to be placed along the perimeter of the corral. How much fencing material is needed?
a. 125 ft
b. 138.5 ft
c. 288.5 ft
d. 438.5 ft
a. 125 ft
b. 138.5 ft
c. 288.5 ft
d. 438.5 ft
1 answer:
Answer : d. 438.5 ft
The diagram for the given statement is attached below.
Two sides AB and AC are equal so the angle B = angle C
WE know sum of three sides of a triangle = 180
angle A + angle B + angle C = 180
55 + B + C = 180
B + C = 180 -55 = 125
B and C are equal so we divide 125 by 2
angle B = 62.5 and angle C = 62.5
Now we apply sin law
150 * sin(55) = sin(62.5) * a
122.8728066 = sin(62.5) * a
a =
a= 138.52 feet
To find perimeter we add all the sides
150 + 150 + 138.52 = 438.52 feet
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