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Find the area of triangle PQR if PQ = QR = 12 and angle PQR = 120 degrees. 

 Jun 14, 2020
 #1
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I assumed that the 120-degree angle is between the two equal sides.

 

Use the law of Cosines to find the 3rd side of the triangle:

 

Obtuse isosceles triangle.

Sides: a = 12   b = 12   c = 20.785

Area: T = 62.354
Perimeter: p = 44.785
Semiperimeter: s = 22.392

Angle ∠ A = α = 30° = 0.524 rad
Angle ∠ B = β = 30° = 0.524 rad
Angle ∠ C = γ = 120° = 2.094 rad

Height: ha = 10.392
Height: hb = 10.392
Height: hc = 6

 Jun 14, 2020
 #2
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We can use the formula \(A = \dfrac12 ab \sin C\) directly.

 

\(A = \dfrac12 \cdot 12^2 \cdot \sin 120^\circ = 72 \cdot \dfrac{\sqrt 3}2 = 36\sqrt 3\)

 Jun 14, 2020

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