From a top-down 2D perspective, a car moves in a diagonal line and travels a distance equivalent to 80 miles. If the angle between the diagonal line and a horizontal reference line is 25 degrees, how far did the car travel horizontally and vertically? If necessary, round your answers to the nearest tenth of a mile. Horizontal distance? Vertical distance?

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22-02-2018
Mathematics

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From a top-down 2D perspective, a car moves in a diagonal line and travels a distance equivalent to 80 miles. If the angle between the diagonal line and a horizontal reference line is 25 degrees, how far did the car travel horizontally and vertically? If necessary, round your answers to the nearest tenth of a mile. Horizontal distance? Vertical distance?

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Rodiak Rodiak · Answer 1 · 2018-02-28T23:46:08+01:00

We can use Pythagorean theorem for right angle triangle to solve this problem.

The diagonal line would be hypothenuze. Horizontal and vertical distance would be other two sides of a triangle.

We will use the following formulas:
[tex]sin \alpha = \frac{opposite}{hypothenuze} \\ cos \alpha = \frac{adjacent}{hypothenuze} [/tex]
Where opposite side is vertical distance and adjacent side is horizontal distance.

Solving for these two sides we have:
[tex]opposite = hypothenuze * sin \alpha \\ adjacent = hypothenuze * cos \alpha [/tex]

We insert numbers and we get solution:
[tex]opposite = 80 * sin 25 = 33.8miles \\ adjacent = 80 * cos 25 = 72.5miles [/tex]