A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{3}$ $(pi)/3$ , and the length of B is 2, 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 $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{3}$ $(pi)/3$ , and the length of B is 2, what is the area of the triangle?

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Answer 1 · 2016-05-10T13:40:53

Area= 0.6685

Explanation:

The triangle ABC and its given components would be as shown in the figure. Angle B= $π - \frac{π}{3} - \frac{π}{8} = \frac{13 π}{24}$ $pi- pi/3-pi/8= (13pi)/24$ . apply sine law to find side a or side c. Let us get a
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a = $2 \frac{sin (\frac{π}{3})}{sin (\frac{13 π}{24})}$ $2sin (pi/3)/ sin ((13pi)/24)$

To find the area length of perpendicular fro B upon side b is required . It would be a $sin (\frac{π}{8})$ $sin (pi/8)$

Area= $(\frac{1}{2}) (2)$ $(1/2) (2)$ a $sin (\frac{π}{8})$ $sin (pi/8)$

= a $sin (\frac{π}{8})$ $sin (pi/8)$ = $2 \frac{sin (\frac{π}{3})}{sin (13 \frac{π}{24})} sin (\frac{π}{8})$ $2 sin(pi/3) /sin(13pi/24) sin (pi/8)$

=0.6685

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{3}$ $(pi)/3$ , and the length of B is 2, 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 π8(pi)/8, the angle between sides B and C is π3(pi)/3, and the length of B is 2, what is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{π}{3}$ $(pi)/3$ , and the length of B is 2, what is the area of the triangle?