A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 3, 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 $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 3, what is the area of the triangle?

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Answer 1 · 2016-03-25T21:14:47

$A r e a \approx 30.766 {units}^{2}$ $Area ~~ 30.766" units"^2" "$ to 3 dp

Explanation:

Tony B

Sum of internal angles for a triangle is $180^{o} \to π radians$ $180^o-> pi" radians"$

So $∠ A C = \frac{1}{24} π \to 7 \frac{1}{2} .^{o}$ $/_AC= 1/24 pi ->7 1/2color(white)(.)^o$

$h = B sin (∠ A B) = 3 sin (\frac{3}{8} π) \approx 2.7716$ $h=Bsin(/_AB) = 3 sin(3/8 pi) ~~2.7716$

$\frac{A}{sin (∠ B C)} = \frac{B}{sin (∠ A C)}$ $" "A/sin(/_BC)=B/sin(/_AC)$

$\Rightarrow A = \frac{B sin (∠ B C)}{sin (∠ A C)} \approx 22.201$ $=> A = (Bsin(/_BC))/sin(/_AC)~~22.201$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$A r e a = \frac{A}{2} \times h$ $Area = A/2xxh$

$A r e a = \frac{B sin (∠ B C)}{2 sin (∠ A C)} \times B sin (∠ A B)$ $Area = (Bsin(/_BC))/(2sin(/_AC))xxBsin(/_AB)$

$A r e a = \frac{3 sin (∠ B C)}{2 sin (∠ A C)} \times 3 sin (∠ A B) \approx 30.766$ $Area = (3sin(/_BC))/(2sin(/_AC))xx3sin(/_AB) ~~ 30.766" "$ to 3 dp

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 3, 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 3π8(3pi)/8, the angle between sides B and C is 7π12(7pi)/12, and the length of B is 3, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{3 π}{8}$ $(3pi)/8$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 3, what is the area of the triangle?