Finding the Area of a Triangle

An Application of Trigonometry

Warm Up !   1. Recall the formula for the area of a triangle

!   2. Find the area of a triangle with base = 12 and height = 5.

10 minutes

End

Homework Check

!   Page 30

Today’s Objective

!   Students will be able to find the area of a triangle when you know two sides lengths and the measure of the included angle.

Area of a Triangle

!   You probably remember how to find the area of a triangle from middle school.

!   In general, the area of a triangle is where b = base and h = height.

!   But what if our triangle doesn’t give us the base or height?

WE CAN USE TRIG!

12bh

Example

!   What’s the base? !   AC = 120

!   What’s the height? !   BD = ???

Example

!  Sin 40° = BD/100

!  BD = 100*sin40°

!  To find the area: !  A = 0.5bh

!  A = 0.5(150)(100sin40°)

!  A ≈ 4821 m2

Practice 1

Practice 2

Vocab Review

!   When showing triangles were congruent, we used the word “included angle” when using SAS.

!   The “included angle” was the angle between the two known sides. Included Angle

What if we know two sides and the included angle…

!   Set up a trig function to find h:

!   Sin C = hb

!   So, h = b Sin C

!   If we find the area of a triangle by: Area = 0.5bh

!   Then A = 0.5(a)(b)(SinC)

Classwork

!   4.9 Area of a Triangle Practice (page 32)

Homework

!   4.9 Area of a Triangle (page 33)