A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 5, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{7 π}{24}$ $(7pi)/24$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 5, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{7 π}{24}$ $(7pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-03-15T02:51:27

The triangle does not exist...
Here's the area anyways:
$A = \frac{5 \sqrt{2}}{2} u n^{2} \approx 3.54 u n^{2}$ $A= (5sqrt2)/2 un^2 approx 3.54 un^2$

Explanation:

Area of the triangle:
$A = \frac{1}{2} a \cdot b \cdot sin C$ $A= 1/2a*b*sinC$
Let's determine angle C:
$\frac{24 π}{24} - \frac{7 π}{24} - \frac{11 π}{24} = \frac{π}{4}$ $(24pi)/24-(7pi)/24-(11pi)/24= pi/4$

Area of the triangle:
$A = \frac{1}{2} (2) (5) sin (\frac{π}{4}) =$ $A= 1/2(2)(5)sin(pi/4)=$
$A = \frac{5 \sqrt{2}}{2} u n^{2} \approx 12.37 u n^{2}$ $A= (5sqrt2)/2 un^2 approx 12.37 un^2$

How do I know this triangle particularly does not exist?
Well:
The law of sines states:
SinA/a= SinB/b
Therefore:
$B = arcsin (\frac{sin A \cdot b}{a})$ $B= arcsin((SinA*b)/a)$
$B = arcsin ⎛ ⎜ ⎝ \frac{sin (\frac{7 π}{24}) \cdot 5}{2} ⎞ ⎟ ⎠ = u n d e f .$ $B= arcsin((Sin((7pi)/24)*5)/2)= undef.$
Since Angle B cannot be computed, this triangle does not exist

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A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 5, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{7 π}{24}$ $(7pi)/24$ . What is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 5, respectively. The angle between A and C is 11π24(11pi)/24 and the angle between B and C is 7π24 (7pi)/24. What is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 5, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{7 π}{24}$ $(7pi)/24$ . What is the area of the triangle?