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6. WORD PROBLEM.

A ship at sea is 70 miles from one radio transmitter and 130 miles from another. The measurement of the
angle between the signals is 130°. To the nearest mile, how far apart are the transmitters?

User Jeannie
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1 Answer

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Final answer:

The distance between the transmitters is approximately 214 miles.


Step-by-step explanation:

To find the distance between the transmitters, we can use the Law of Cosines. Let's call the distance between the ship and the first transmitter x and the distance between the ship and the second transmitter y. We can use the formula: c^2 = a^2 + b^2 - 2ab * cos(C), where a = 70, b = 130, and C = 130°. Plugging in these values, we get: c^2 = 70^2 + 130^2 - 2 * 70 * 130 * cos(130°). Evaluating this, we find that c^2 ≈ 45936 and thus c ≈ sqrt(45936). Rounding to the nearest mile, the distance between the transmitters is approximately 214 miles.


Learn more about Finding the distance between two points

User DIG
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