A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?

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Answer 1 · 2017-05-01T06:54:40

Sum of angles in a triangle, followed by
Sin rule

Explanation:

since we know 2 angles of the triangle and the length of one side of the triangle (assuming it is measured in centimetres), the first step we can take is

$π$ $pi$ - $\frac{3 π}{4}$ $(3pi)/4$ - $\frac{π}{12}$ $(pi)/12$ = 3rd unknown angle, $x$ $x$

We can then apply the sin rule to find the length of either A or C (I'll go with C)

$\frac{C}{sin (\frac{3 π}{4})}$ $C/sin((3pi)/4)$ = $\frac{7}{sin (x)}$ $7/sin(x)$

area of the triangle = 0.5 (7)(C) $sin (\frac{π}{12})$ $sin(pi/12)$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is 3π4(3pi)/4 and the angle between sides B and C is π12pi/12. If side B has a length of 7, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?