PQ= x cm PR= 2xcm Angle QPR= 30 degrees The area of the triangle PQR= Acm squared Show that x = square root 2A?

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Answer 1 · 2018-05-27T13:03:15

See below.

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Area of triangle is #1/2"base"xx"height"#

From the diagram we can see we need to find h:

Using the sine function:

#sin(30)="opposite"/"hypotenuse"=h/x#

Therefore:

#h=xsin(30)#

base = 2x:

#"Area" = 1/2(2x)xsin(30)=A#

#1/2(2x^2)sin(30)=A#

#sin(30)=1/2#

#:.#

#1/2(2x^2)(1/2)=A#

#1/2x^2=A#

#x^2=2A=>x=sqrt(2A)#