Question

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

Answer 1

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

$\frac{sin A}{a} = \frac{sin B}{b}$

$\frac{sin 55}{a} = \frac{sin 62.5}{150}$

150 * sin(55) = sin(62.5) * a

122.8728066 = sin(62.5) * a

a = $\frac{ 122.8728066}{sin(62.5)}$

a= 138.52 feet

To find perimeter we add all the sides

150 + 150 + 138.52 = 438.52 feet