Question

Need help answering these, with work please

Answer 1

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:

brainly.com/question/16955971

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