Maria is erecting a statue on a triangular plot of land. She wants to put decorative stonework edging around the site. The lengt
h 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.
1 answer:
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).
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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