Question

In a cirlce `H`, if `angleDHG=(11x-36)^\circ` and `angleGHF=(x+12)^\circ`, find `hat{DG}`? I've found `x=17` and the `angleDHG=151^\circ`. Would you please help me on the next step to find the arc length?

Answer 1

You've already figured it out.

`mhat {DG}=151^{\circ}`

Explanation:

An arc’s length means the same commonsense thing length always means — you know, like the length of a piece of string (with an arc, of course, it’d be a curved piece of string).

Make sure you don’t mix up arc length with the measure of an arc which is the degree size of its central angle.

In this above given figure, we have measure of the arc `hat {AB}=45^{\circ}`.

Remember, the degree measure of an arc is written like `mhat{AB}`.

If we were to find the length of the arc `hat {AB}`, we would be using the formula:

`\text{Arc Length } m hat{AB} = ((mhat{AB})/360^{\circ})\cdot 2\pi r`