Question

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?

Answer 1

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.

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