Choose one of the following trig application problems. 5. A ferry is used to transport guests from the dock to two hotels across a large lake. The hotels are located 550 m apart from each other.The first hotel is at a 49 degree angle between the dock and the second hotel. The second hotel is at a 56 degree angle between the dock and the first hotel. How far is each hotel from the dock? ( 6 marks)

Question

Choose one of the following trig application problems. 5. A ferry is used to transport guests from the dock to two hotels across a large lake. The hotels are located 550 m apart from each other.The first hotel is at a 49 degree angle between the dock and the second hotel. The second hotel is at a 56 degree angle between the dock and the first hotel. How far is each hotel from the dock? ( 6 marks)

Answer 1

### The first hotel is approximately 472.58m from the dock, and the second hotel is approximately 428.67m from the dock.

Answer 2

## Step 1: Visualizing the Problem### We have a triangle formed by the dock and the two hotels. Let D be the dock, H1 be the first hotel, and H2 be the second hotel. We are given the distance H1H2 = 550m, angle DH1H2 = 49°, and angle DH2H1 = 56°. We need to find DH1 and DH2.## Step 2: Finding the remaining angle### The sum of angles in a triangle is 180°. Therefore, angle H1DH2 = 180° - (49° + 56°) = 180° - 105° = 75°.## Step 3: Applying the Sine Rule### The sine rule states that

. In our case, we have:

## Step 4: Calculating DH1###

m## Step 5: Calculating DH2###

m

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