A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $35$ $35$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , 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 $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $35$ $35$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?

1 Answer

Impact of this question

1429 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-26T03:10:43

$Lengths of sides a = b = 18.12 units$ $color(purple)("Lengths of sides " a = b = 18.12 " units"$

Explanation:

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/]( useruploads.socratic.org )

$ˆ C = \frac{5 π}{6}, ˆ A = \frac{π}{12}, c = 35$ $hat C = (5pi)/6, hat A = pi/12, c = 35$

$ˆ B = π - \frac{5 π}{6} - \frac{π}{12} = \frac{π}{12}$ $hat B = pi - (5pi)/6 - pi/12 = pi/12$

It's an isosceles triangle with sides a & b equal.

Applying Law of Sines,

$a = b = \frac{c \cdot sin A}{sin C} = \frac{35 \cdot sin (\frac{π}{12})}{sin (\frac{5 π}{6})} = 18.12 units$ $a = b = (c * sin A) / sin C = (35 * sin (pi/12)) / sin ((5pi)/6) = 18.12 "units"$

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $35$ $35$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , 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 (5pi)/65π6(5pi)/6. If side C has a length of 35 3535 and the angle between sides B and C is pi/12π12pi/12, 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 $\frac{5 π}{6}$ $(5pi)/6$ . If side C has a length of $35$ $35$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?