If the owner wants to paint the deck area, how many square feet of paint will they need to purchase? Your answer should be rounded to the nearest tenth if necessary.

Approximately 14.647147438893 meters

Round this value however you need.

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Explanation:

Refer to the diagram below. The blue horizontal line is the water surface, and just below that are points A and B to represent diver 1 and diver 2 respectively. Point C is the shark's location. The diagram is not to scale. The assumption is that the two divers are at the same depth in the water.

Angle A (also known as angle BAC or CAB) is the angle formed at diver 1's location, which is the 47 degree angle mentioned earlier. Angle B is 40 degrees. This must mean angle C is 180-A-B = 180-47-40 = 93 degrees. Note how A+B+C = 47+40+93 = 180.

The goal is to find the distance from diver 2 to the shark. So we want the distance from point B to point C. In other words, we want the length of segment BC. Since this segment is opposite angle A, we'll refer to this side as lowercase 'a'. The lowercase letters represent side lengths and they are conventionally opposite the uppercase letter angles. So side b is opposite angle B, and side c is opposite angle C.

Here's what we have so far:

We can apply the law of sines to find side 'a'.

a/sin(A) = c/sin(C)

a/sin(47) = 20/sin(93)

a = sin(47)*( 20/sin(93) )

a = 14.647147438893

Make sure your calculator is in degree mode.

The distance from diver 2 to the shark is approximately 14.647147438893 meters. Round this value however you need.