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Solving Triangle Distances Between Fire Towers A and B

This exercise illustrates how to find angles A, B, and F in a triangle formed by two fire towers and a fire site. Tower A is located at a bearing of 329°, and Tower B at 295°, with various angles provided (angle A = 50°, angle B = 65.45°, angle F = 81°). Using these angles, we calculate the distances from the fire to each tower: 73 miles from Tower A and 79 miles from Tower B. The problem emphasizes application of trigonometric principles in navigation and distance measurement.

aaron-robinson
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Solving Triangle Distances Between Fire Towers A and B

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  1. MathXL, section 7.1, #9 To view this powerpoint, click on the screen and select “full screen”.

  2. Draw the picture Fire Tower B 295o 45 miles 50o Tower A 329o

  3. Find angle A, angle Band angle F. F B 65o 45 81o A Angle A 50o 329o 295o Angle B 50o Angle A = 360 – 329 + 50 Angle B = 295 – 180 – 50

  4. Solve the triangle. F F = 180 – 81 – 65 34o BF = 79 miles B 65o 45 81o AF = 73 miles A The distance from tower A to the fire is 73 miles and from tower B to the fire is 79 miles.

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