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Maria is erecting a statue on a triangular plot of land. She wants to put decorative stonework edging around the site. The length of one side of the plot of land is 25 feet. If the angles at the end of this side are 65° and 38°, find the length of stonework edging needed to enclose the site on which the statue is erected.

Respuesta :

Draw the triangle shown below to illustrate the problem.
Given:
a=25 ft, ∠B=65°, ∠C=38°.

Because angles in a triangle sum to 180°, therefore
∠A = 180 - 65 - 38 = 77°.

Apply the Law of Sines to find b and c.
b/sin(B) = a/sin(A)
b/sn(65°) = 25/sin(77°)
b = [sin(65)/sin(77)]*25 = 23.254 ft

c/sin(C) = a/sin(A)
c/sin(38) = 25/sin(77)
c = [sin(38)/sin(77)]*25 = 15.796 ft

The length of stone work required is
a + b + c
= 25 + 23.254 + 15.796
= 64.05 ft

Answer: 64 ft (nearest integer).
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