# ISEE Upper Level Math : How to find the length of an arc

## Example Questions

### Example Question #1 : How To Find The Length Of An Arc

A giant clock has a minute hand six feet long. How far, in inches, did the tip move between noon and 1:20 PM?      Explanation:

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius 6 feet. This circumference is feet. One hour and twenty minutes is hours, so the tip of the hand moved feet, or inches.

### Example Question #2 : How To Find The Length Of An Arc

A giant clock has a minute hand three feet long. How far, in inches, did the tip move between noon and 12:20 PM?   It is impossible to tell from the information given  Explanation:

The distance that the tip of the minute hand moves during one hour is the circumference of a circle with radius feet. This circumference is feet. minutes is one-third of an hour, so the tip of the minute hand moves feet, or inches.

### Example Question #3 : How To Find The Length Of An Arc In the above figure, express in terms of .     Explanation:

The measure of an arc - - intercepted by an inscribed angle - - is twice the measure of that angle, so       ### Example Question #4 : How To Find The Length Of An Arc In the above diagram, radius .

Give the length of .     Explanation:

The circumference of a circle is multiplied by its radius , so . , being an inscribed angle of the circle, intercepts an arc with twice its measure: The length of is the circumference multiplied by : .

### Example Question #5 : How To Find The Length Of An Arc

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?     Explanation:

While visiting a history museum, you see a radar display which consists of a circular screen with a highlighted wedge with an angle of . If the screen has a radius of 4 inches, what is the length of the arc of the highlighted wedge?

To begin, let's recall our formula for length of an arc. Now, just plug in and simplify  