Datasheet

Area of a Triangle and Circular Sector Teacher Notes
Topic Area: Trigonometric Applications
NCTM standards:
• Develop fluency in operations with real numbers using technology for more-
complicated cases.
• Understand functions by interpreting representations of functions.
Objective
To calculate the area of a triangle and a circular sector using trigonometry.
Getting Started
In this activity, the student will learn how to calculate the area of a triangle
and a circular sector using trigonometry. The area of a triangle is defined to
be one-half the product of the lengths of the two sides (a, b) and the sine of
angle (C) included between those two sides. The formula looks like:
Activity 8 • Pre-Calculus with the Casio fx-9750GII
area =
2
1
•a•b•sin C
a
C
b
Another useful formula for finding the area of a triangle is Heron’s formula In
this formula the students need to know the lengths of the three sides (
a, b, c)
to find the area of the triangle. Heron’s formula is:
area =
))()(( csbsass −−− where s =
2
1
(a + b + c)
b

c
a

The area of a circular sector is defined to be one-half of the product of the
radius (r) squared and the central angle. The formula is:
area =
2
1
• r
2
•
θ
or
θ

r 
θ

r 