A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ , 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?

Question

A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ , 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?

1 Answer

Impact of this question

1681 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-17T03:52:19

$A_{t} = (\frac{1}{2}) \cdot 2.4495 \cdot 2 \cdot sin (\frac{5 π}{12}) = 2.366$ $A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366$

Explanation:

Given : $b = 2, ˆ A = \frac{π}{3}, ˆ C = \frac{5 π}{12}$ $b = 2, hatA = pi/3, hatC = (5pi)/12$

$ˆ b = π - (\frac{π}{3} + \frac{5 π}{12}) = \frac{π}{4}$ $hatb = pi - (pi/3 + (5pi)/12) = pi/4$

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b / sin B = c / sin C$

$a = \frac{b \cdot sin A}{sin B} = \frac{2 \cdot sin (\frac{π}{3})}{sin ((\frac{π}{4}) = 2.4495}$ $a = (b * sin A) / sin B = (2 * sin (pi/3)) / sin ((pi/4) = 2.4495$

enter image source here

$A_{t} = (\frac{1}{2}) a b sin C$ $A_t = (1/2) a b sin C$

$A_{t} = (\frac{1}{2}) \cdot 2.4495 \cdot 2 \cdot sin (\frac{5 π}{12}) = 2.366$ $A_t = (1/2) * 2.4495 * 2 * sin ((5pi)/12) = color (red)(2.366$

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ , 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?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. If the angle between sides A and B is 5π12(5pi)/12, the angle between sides B and C is π3pi/3, and the length of B is 2, what is the area of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ , 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?