7-2 (whatever this title may be)

I am going to be reviewing 7-2. These steps and formulas are most commonly used to solve different word problems. There are several formulas that you will have to remember in order to properly solve these word problems.

The first formula is as follows:

K=1/2r^2 Ɵ

In this equation, k is the area of a sector, r is the radius, and Ɵ is the central angle.

The second formula is follows:

K=1/2rs

In this equation, r is the radius, and arc is the length.

Another equation within this section is that for apparent size. That equation is as follows:

s=rƟ

In this formula, r=distance between two objects, Ɵ=apparent size, and S=diameter of an object.

EXAMPLE 1:

A sector of a circle has a radius 6 cm and central angle 0.5 radians. Find its arc length and area.

In this problem,

R(radius)=6cm

Ɵ(central angle)=.5

K(area)=?

S(arc length)=?

To solve this problem, you would use the equation k=1/2r^2Ɵ. Therefore, k=1/2(6)^2(.5) so k=9cm^2. You then plug into k=1/2rs. Since you’re solving for s, it becomes k/1/2r=s. Therefore s=9/3 so s=3cm.

So, in the end the arc length (s) is 9cm and the area (k) is 9cm^2.

--Sarah