MathsPBAT - Name:TurjoChowdhury Algebra2/Trig Aim...

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Name: Turjo ChowdhuryAlgebra 2/TrigAim: How can angles help us find the area of a triangle?Objective: Students will learn how to:­Find Area of triangles without knowing its height.­Find angles and sides of a triangle.­Use the Law of Sines.Core Mathematical Standards :­CCSS.MATH.CONTENT.HSG.SRT.D.9Derive the formulaA= 1/2absin(C) for the area of a triangle by drawing an auxiliary line from avertex perpendicular to the opposite side.­A2.A.74Determine the area of a triangle or parallelogram given the measure of two sides and theincluded angle.­CCSS.MATH.CONTENT.HSG.SRT.11Understand and apply the Law of Sines to find unknown measurements in right and non­righttriangles.Do Now:1.Find the area of a triangle when the height=30 cm and the base= 15 cm­to find the area:Area=x base x height21=0.5 x 15 x 30=225mc22.Find the height of a triangle when the area=150and base= 10 cmmc2We know,Area=x base x height21
Therefore,Height=Base2 ×Area=102 ×150=10300=30 cm3. Side Measurement in cm.Find in 2 decimal places:­the side a­the angle X­the area of the triangle­to find a,
a[Pythagoras Theorem]2= 72− 5295a2= 4− 2a= √24cm.90a= 4­to find the angle XSin(x)=75X=(5/7)inS−1X=degrees5.584­to find the area:base=5 and height=4.90Area=x base x height21=0.5 x 5 x 4.90=12.25mc2
Motivation:What is the area of a triangular region of wetland? Explain your thinking.(Hint:Even though swamp and thick vegetation prevent you from making moremeasurements you can still find a height of the triangle.)For the height, a line can be drawn from the mid point of the line AB connecting to thepoint C. The line can be named h. h would be perpendicular to AB.
To find h,Sin() =04h280h=280 x Sin(40)h= 179.98 ft (correct to 2 decimal place)Therefore, we can find the area of this triangular wetland by using the formulaArea=x Base x Height21The base here is the line ABArea= 0.5 x 420 x 179.98= 37,796(Nearest whole number)tf2Vocabulary:

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Term
Spring
Professor
Oshira Martinez
Tags
Algebra, Trigonometry, Triangles And Right Triangles, Sin, Pbat, Sines, Square inch, Square metre

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