Question

on a distant​ planet, a central angle intercepts an arc of miles. what is the radius of the planet at its​ equator?

Answer 1

If on a distant​ planet, a 10° central angle intercepts an arc of (136π) miles, then the radius of the planet at its​ equator is 2448 Miles.

As per the question-statement, on a distant​ planet, a 10° central angle intercepts an arc of (136π) miles. [Refer to the photo attached]

We are required to find the radius of the planet at its​ equator based on the above data.

To solve this question, we need to know the relation between arc length, radius and angle, and we will form a linear equation in one variable, based on the conditions mentioned in the question statement, and solving the equation, we will obtain our desired answer

[Arc length = (Radius * Angle)],

We are already provided with data about the arc length (136π miles) and central angle (10°), and let us assume radius of the planet be "r".

We will convert the central angle from degrees to radians, i.e.,

10° = $\frac{180}{18}=\frac{\pi }{18} rads$.

Now, using the data provided in the question statement about arc length and central angle, and our assumed radius in the relation between arc length, radius and angle, we get

$136\pi =(r*\frac{\pi }{18} )\\or, r = \frac{136\pi }{\frac{\pi }{18} } \\or, r = 136\pi * \frac{18}{\pi} \\or, r = (136*18) = 2448$ miles.

Therefore, radius of the planet at its​ equator is 2448 Miles.

• Linear Equation: In Mathematics, a linear equation is an algebraic equation which when graphed, always results in a straight Line and thus, comes the name "Linear". Here, each term has an exponent of 1 and is often denoted as (y = mx + c)  where, 'm' is the slope and 'b' is the y-intercept. Occasionally, it is also called as a "linear equation of two variables," where y and x are the variables.
• Arc: An arc is a part of the circumference of a circle or of any over curve.

To learn more about Arc lengths, click on the link below.

brainly.com/question/16403495

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