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In a triangle PQR, side PQ=3, and side PR=2cm. The area of the triangle PQR is 2cm^2.

State two possible values for angle QPR (in degrees).

 Feb 17, 2021
 #1
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Here's  one way to do this  :

 

Let  P = (0,0)

Let Q  =  (3,0)

Connstruct  a circle centered at  P   with  a radius  of  2

 

The  equation is    x^2  + y ^2   = 4

 

Let the base of  PQR  =  PQ   = 3

So....the height of  PQR  can be found  as

 

2 = (1/2) 3  *  height

2  = 3/2  * height

height  = (2/3)(2)  =4/3

 

Sub  this into  the  equation of  the  circle   for  y

 

x^2 +  (4/3)^2  = 4

x^2  + 16/9  = 4

 

x^2   =  (36 - 16)  /9

 

x^2  =  20  / 9      take both roots

 

x = sqrt (20)/3   =   (2/3) sqrt (5)

 

x =  - sqrt(20)/3 = (-2/3)sqrt (5)

 

So  ....as  shown  in the  figure

 

 

R1   =   ( -(2/3)sqrt 5  ,4/3)

R2  = ( (2/3)sqrt (5)  ,4/3)

 

Possible  angle  values of QPR  ≈  41.81°    and  ≈ 138.19°

 

 

cool cool cool

 Feb 17, 2021

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