Cot(x) = 3.2404 How would you solve for x?

Mathematics

1 answer:

HACTEHA [7]3 years ago

7 0

Cot (x) = 3.2404
1/tan(x) = 3.2404
tan(x) = 1 / 3.2404
x = inverse tangent ( 1 / 3.2404 )
x = 72.8 degrees (3 s.f.)

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A car wheel has a radius of 16 inches. Through what angle ( to the nearest tenth of a degree ) does the wheel turn when the car

olya-2409 [2.1K]

First of all, let's convert all the measures to the same unit: 4 feet are 48 inches.

Now, as the wheel turns, there is a proportion between the angle and the distance travelled: for example, when the car moves forward a whole circumference, the angle will be 360°. Conversely, if the wheel turns 180°, then the car will move forward a distance which is half the circumference of the wheel, and so on.

Since the radius is 16 inches, the circumference will be

$C=2\pi r = 32\pi$

So, we have the following proportion:

$360\div 32\pi = x \div 48$

that you can read as: "if an angle of 360 corresponds to a distance travelled of $32\pi$ , then the unknown angle x corresponds to a distance travelled of 48 inches.