Spcial right triangle problem: The diagonal of a rectangle makes an angle of 60 with one of the sides of the rectangle. if the side adjacent to the 50 angle measures 16 cm,find the perimeter of the rectangle.

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should it be adjacent to the 60 angle, and not 50 angle?  I assure you, with the given data, there is no 50 angle here :-)

Answers

  • Brainly User
2016-02-10T01:14:24+08:00
Given: 
     θ = 60°
     side (width) adjacent θ = 16 cm
     side (length) opposite θ = x

Equation:

     tan θ = opposite / adjacent

     tan 60° = x / 16 cm

     x = (tan 60°) (16 cm)

     x = (1.732) (16 cm)

     x = 27.712  or  28 cm    ⇒  Length = 28 cm
   
Solve for perimeter of the rectangle:

     P = 2 (length) + 2 (width)

     P = 2 (28 cm) + 2 (16 cm)
   
     P = 56 cm + 32 cm
   
     P = 88 cm

ANSWER:  The perimeter of rectangle is 88 cm.

CLICK image below to view the illustration rectangle with its diagonal.

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