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

Question

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

1 Answer

Impact of this question

1306 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-04T07:50:34

The lengths of the sides are $A = 0.88$ $A=0.88$ and $B = 2.29$ $B=2.29$

Explanation:

We apply the sine rule to the triangle $A B C$ $ABC$ .

$\frac{A}{sin ˆ A} = \frac{B}{sin ˆ B} = \frac{C}{sin ˆ C}$ $A/sin hat A=B/sin hat B=C/ sin hatC$

The angle $ˆ B$ $hat B$ is

$= π - (ˆ A + ˆ C)$ $=pi-(hatA+hatC)$

$= π - (\frac{1}{3} π + \frac{1}{8} π) = π - \frac{11}{24} π = \frac{13}{24} π$ $=pi-(1/3pi+1/8pi)=pi-11/24pi=13/24pi$

Therefore,

$\frac{A}{sin (\frac{1}{8} π)} = \frac{B}{sin (\frac{13}{24} π)} = \frac{2}{sin (\frac{1}{3} π)} = 2.31$ $A/sin(1/8pi)=B/sin(13/24pi)=2/sin(1/3pi)=2.31$

$A = 2.31 \cdot sin (\frac{1}{8} π) = 0.88$ $A=2.31*sin(1/8pi)=0.88$

$B = 2.31 \cdot sin (\frac{13}{24} π) = 2.29$ $B=2.31*sin(13/24pi)=2.29$

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. The angle between sides A and B is π3(pi)/3. If side C has a length of 22 and the angle between sides B and C is π8( pi)/8, what are the lengths of sides A and B?

1 Answer

Explanation:

Related questions

Impact of this question

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