finding the area of a triangle - pbworks 4 day... · warm up ! 1. recall the formula for the area...
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Finding the Area of a Triangle
An Application of Trigonometry
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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
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Homework Check
! Page 30
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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.
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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
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Example
! What’s the base? ! AC = 120
! What’s the height? ! BD = ???
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Example
! Sin 40° = BD/100
! BD = 100*sin40°
! To find the area: ! A = 0.5bh
! A = 0.5(150)(100sin40°)
! A ≈ 4821 m2
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Practice 1
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Practice 2
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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
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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)
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Classwork
! 4.9 Area of a Triangle Practice (page 32)
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Homework
! 4.9 Area of a Triangle (page 33)