If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is $\frac{2 π}{3}$ $(2pi)/3$ , then what is the area of the triangle?

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If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is $\frac{2 π}{3}$ $(2pi)/3$ , then what is the area of the triangle?

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Answer 1 · 2018-01-16T12:26:15

The area is $\frac{\sqrt{3}}{2}$ $sqrt3/2$ ; or, *0.866 *

Explanation:

You'll need the sine rule for area of the triangle.
The formula is:
Area of the $△ A B C = \frac{1}{2} \cdot a \cdot b \cdot sin C$ $triangleABC = 1/2*a*b*sin C$
This drawing(sorry if it's clumsy) will show what I mean :
enter image source here
Here, $∠ C = \frac{2 π}{3}$ $angle C = (2pi)/3$
$sin C = \frac{\sqrt{3}}{2}$ $sin C= sqrt 3/2$
Plugging in the values;
a=1;
b=2;
$sin {\frac{2 π}{3}} = \frac{\sqrt{3}}{2}$ $sin {(2pi)/3} = sqrt3/2$
Area of $△ A B C = \frac{1}{2} \cdot 1 \cdot 2 \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{2}$ $triangle ABC = 1/2*1*2*sqrt3/2 =sqrt3/2$
*Do not forget to give the units...

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If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is $\frac{2 π}{3}$ $(2pi)/3$ , then what is the area of the triangle?

1 Answer

Explanation:

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If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is 2π3(2pi)/3, then what is the area of the triangle?

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Explanation:

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If sides A and B of a triangle have lengths of 1 and 2 respectively, and the angle between them is $\frac{2 π}{3}$ $(2pi)/3$ , then what is the area of the triangle?