Question

You are on a hike. Your camp is 13.0 km away, in the direction 45.0° north of east. You must walk due north to avoid walking through a bog. If you walk due north for 7.0 km, how far, and in what direction, would you have to walk to reach your camp?

Answer 1

To reach the camp from the last position, you must walk 10.95 km due East.

Distance you must walk to reach the camp

The distance you must walk to reach the camp is calculated by applying Pythagoras theorem as follows;

Due north distance, a = 7 km

North east distance, b = 13 km

$b^2 = x^2 + a^2\\\\x^2 = b^2 - a^2\\\\x = \sqrt{b^2 - a^2} \\\\x = \sqrt{13^2 - 7^2} \\\\x = 10.95 \ km$

Thus, to reach the camp from the last position, you must walk 10.95 km due East.

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