on a distant planet, a central angle intercepts an arc of miles. what is the radius of the planet at its equator?
1 answer:
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° = .
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
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.
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