A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 9, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 9, what is the area of the triangle?

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Answer 1 · 2016-04-03T10:45:48

The Area of the triangle $= 20.25$ $=20.25$ units

Explanation:

Opposite angle of side C is $∠ C = \frac{π}{4} = \frac{180}{4} = 45^{0}$ $/_C=pi/4=180/4=45^0$
Opposite angle of side A is $/_A=pi/4=180/4=45^0 :./_B=180-(45+45)=90^0$ Using sine law $A/sinA=B/sinB or A=9*(sin45/sin90)=9/sqrt2$ Since it is a right angled isocelles triangle, Side $B=9/sqrt2$ The Area of the triangle $= 1/2*C*A$ or Area $=1/2*9/sqrt2*9/sqrt2 = 81/4 =20.25$ Units[Ans]

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 9, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{4}$ $pi/4$ , and the length of B is 9, what is the area of the triangle?