An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths f
rom point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and angle B is 125°, diagram not to scale Archaeological Site a. Find the length of AC
1 answer:
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Answer:
Option D) c = 100, a = 50, s = 20
Step-by-step explanation:
we have
6c + 7a + 2s = 990 -----> equation A
3c + 3a + 4s = 430 -----> equation B
2c + 4a + 4s = 480 ----> equation C
Isolate variable s in equation A
2s = 990 -6c-7a
s=495-3c-3.5a -----> equation D
Substitute equation D in equation B and in equation C
3c + 3a + 4(495-3c-3.5a) = 430
3c + 3a +1,980-12c-14a= 430
-9c-11a=-1,550 -----> equation E
2c + 4a + 4(495-3c-3.5a) = 480
2c+4a+1,980-12c-14a=480
-10c-10a=-1,500 -----> 10c+10a=1,500 -----> equation F
Solve the system of equations E and F by graphing
using a graphing tool
Let
The variable c -----> the x-axis
The variable a ----> the y-axis
The solution is the point (50,100)
see the attached figure
so
c=50, a=100
Find the value of s
s=495-3(50)-3.5(100)=-5 -----> is not make sense
therefore
Let
The variable c -----> the y-axis
The variable a ----> the x-axis
The solution is the point (50,100)
so
a=50, c=100
Find the value of s
s=495-3(100)-3.5(50)=20
therefore
The solution is
c=100,a=50,s=20
