WEBVTT
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The shown diagram represents a satellite calculating the distances and the angle.
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Find the distance between the two cities.
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Give your answer to one decimal place.
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Note that the diagram is not to scale.
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In order to solve this problem, we need to calculate the length π₯, the distance between the two cities.
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As we have created a triangle, we can use the cosine rule to find the missing length.
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The cosine rule states that π squared is equal to π squared plus π squared minus two ππ multiplied by cos of π.
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In our example, π is π₯, the unknown, or the distance between the two cities, π is 370 kilometers, π is 350 kilometers, and the angle π is 2.1 degrees.
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Substituting these values into the formula gives us π₯ squared is equal to 370 squared plus 350 squared minus two multiplied by 370 multiplied by 350 multiplied by cos of 2.1.
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Typing the right-hand side into the calculator gives us a value of π₯ squared of 573.946.
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Square rooting both sides of this equation gives us π₯ is equal to 23.957.
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As weβre asked to give our answer to one decimal place, π₯ is equal to 24.0.
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This means that the distance between the two cities is 24 kilometers or 24.0 kilometers.