The side lengths are:
- AC in (5) is 40.88 inches
- AC in (6) is 11.00 yards
- AB in (7) is 24.10 centimeters
- BC in (8) is 27.99 inches
How to solve the side lengths?
Figure 5
To calculate AC, we use the following law of sines.
AC/sin(B) = BC/sin(A)
This gives
AC/sin(144) = 18/sin(15)
Multiply both sides by sin(144)
AC = sin(144) * 18/sin(15)
Evaluate
AC = 40.88
Hence, the side length AC in (5) is 40.88 inches
Figure 6
To calculate AC, we use the following law of sines.
AC/sin(B) = BC/sin(A)
This gives
AC/sin(14) = 31/sin(137)
Multiply both sides by sin(14)
AC = sin(14) * 31/sin(137)
Evaluate
AC = 11.00
Hence, the side length AC in (6) is 11.00 yards
Figure 7
To calculate AB, we use the following law of sines.
AB/sin(C) = BC/sin(A)
Where:
A = 180 - B - C --- angles in a triangle
This gives
A = 180 - 138 - 22
A = 20
So, we have:
AB/sin(22) = 22/sin(20)
Multiply both sides by sin(22)
AB = sin(22) * 22/sin(20)
Evaluate
AB = 24.10
Hence, the side length AB in (7) is 24.10 centimeters
Figure 8
To calculate BC, we use the following law of sines.
BC/sin(A) = AC/sin(B)
Where:
B = 180 - A - C --- angles in a triangle
This gives
B = 180 - 58 - 33
B = 89
So, we have:
BC/sin(58) = 33/sin(89)
Multiply both sides by sin(58)
BC = sin(58) * 33/sin(89)
Evaluate
BC = 27.99
Hence, the side length BC in (8) is 27.99 inches
Read more about law of sines at:
https://brainly.com/question/16955971
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