# Pre-Calc arc length notes ```Pre-Calc tues 10/14

Goals
1. Calculate the area and arc length of a
sector
2. Use arc length to estimate the size of
distant objects.
Problem solving

 We used a problem solving strategy to lead us to the
idea of apparent size, and knowledge of when we
might use it.
Problem solving from
the beginning

What question do you want to answer?
What do you need to answer it?
Arc length

 The arc length of a sector, s, is given by the formula
 𝑠 = 𝑟𝜃, when theta is given in radians.
𝑠 =
𝜃
360
∗ 2𝜋𝑟, when theta is given in degrees
Area of a sector

 The area of a sector, K, is:
1
2
 𝐾 = 𝑟 2 𝜃, when theta is given in radians
𝐾 =
𝜃
360
∗ 𝜋𝑟 2 , when theta is in degrees
Apparent size

 The apparent size is the angle an object subtends
with your eye, when viewed from a distance.
 The height or diameter of an object can be estimated
using arc length, with apparent size as the central
angle of the sector.
 Distance from the observer to the object is the radius
of the sector.
 For small central angles the approximation is quite
close.