Which equation gives the length of an arc, s, intersected by a central angle of 3 radians in a circle with a radius of 4 in.?

12 in

Step-by-step explanation:

the arc length formula is s = rФ, where Ф is the central angle in radians.

Here, the arc length is s = (4 in)(3 radians) = 12 in

There is no any option, but the question is answerable. The length of an arc of a circumference is a fraction of that circumference. Recall that a circumference measures 360 degrees. Suppose you have an arc whose central angle degrees, then the arc of a circumference can be found as:

So in this case, the expression:

represents the fraction we are talking about.

B. AD = sqrt(CD * BD)

Step-by-step explanation:

By the right triangle altitude theorem,

CD/AD = AD/BD

AD^2 = CD * BD

AD = sqrt(CD * BD)

B. AD = sqrt(CD * BD)

B

Step-by-step explanation:

In this question, you are clearly supposed to use the geometric mean theorem or known as the right triangle altitude theorem. But note that there are other approaches to find the height of the triangle.

Using Pythagorean theorem:

Also,