Secant Angles

Don't try this at home, Shmoopers.

CirclesTangents and Secants
GeometryAngles
LanguageEnglish Language

Transcript

00:23

To test whether his vehicles are capable of traveling in exactly straight paths…

00:27

…Roger will have the vehicles take off on two routes that form an angle of 45 degrees.

00:33

They will reach the lake at two points, forming an arc of 60 degrees…

00:37

…and then they’ll continue their respective paths across the lake,

00:40

arriving somewhere on the opposite shore.

00:42

If their journey is successful and the vehicles travel in perfectly straight lines…

00:47

…what should be the arc measure between them when they arrive on the far shore of the lake?

00:55

The formula for finding any arc or angle measure involved in a secant angle problem such as this…

01:01

...is secant angle K equals one-half the difference between the measurements of the

01:06

far arc A-B-C and near arc X-Y-Z.

01:10

With this formula, it’s a simple matter of… plugging in.

01:13

The secant angle of 45 degrees equals 1/2 the difference between the measurement of

01:17

the far arc – that’s our unknown…

01:20

…and the near arc measurement of 60 degrees here.

01:23

Multiply both sides of the equation by 2 to cancel out the 1/2 on the right side.

01:27

45 times 2 equals 90, so you get 90 degrees on the left side...

01:31

equals arc A-B-C minus 60 degrees.

01:34

Add 60 degrees to both sides of the equation and we have the solution:

01:38

Arc A-B-C should be 150 degrees… if the experiment goes as intended.

01:44

Now that all of the theoretical measurements are in order, Roger’s ready to begin the test.

01:48

Perhaps he should have factored in a few more variables… like… actual geese, for example.

01:53

This has turned into a real honk-fest.