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pav-90 [236]
3 years ago
15

From a top-down 2D perspective, a car moves in a diagonal line and travels a distance equivalent to 80 miles. If the angle betwe

en 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?
Mathematics
1 answer:
SVEN [57.7K]3 years ago
3 0
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:
sin \alpha  =  \frac{opposite}{hypothenuze}  \\ cos \alpha = \frac{adjacent}{hypothenuze}
Where opposite side is vertical distance and adjacent side is horizontal distance.

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

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