A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 7, 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 $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 7, what is the area of the triangle?

1 Answer

Impact of this question

1520 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-07T17:00:05

$= 79.16$ $=79.16$

Explanation:

This is a triangle where side $B = 7$ $B=7$ is opposite of the
Angle [ $π - (\frac{π}{3} + 7 \frac{π}{12})] = π - 11 \frac{π}{12} = \frac{π}{12}$ $pi-(pi/3+7pi/12)]=pi-11pi/12=pi/12$
Therefore
$\frac{B}{sin (\frac{π}{12})} = \frac{C}{sin (\frac{π}{3})}$ $B/sin(pi/12)=C/sin(pi/3)$
or
$\frac{7}{sin (\frac{π}{12})} = \frac{C}{sin (\frac{π}{3})}$ $7/sin(pi/12)=C/sin(pi/3)$
or
$C = 7 \frac{sin (\frac{π}{3})}{\frac{sin π}{12}}$ $C=7sin(pi/3)/(sinpi/12)$
or
$C = 7 (3.34)$ $C=7(3.34)$
or
$C = 23.42$ $C=23.42$
$H e i g h t$ $Height$ of the triangle is $= 7 sin (π - 7 \frac{π}{12}) = 7 sin (5 \frac{π}{12}) = 6.76$ $=7sin(pi-7pi/12)=7sin (5pi/12)=6.76$
Therefore
Area of the triangle $= \frac{1}{2} (C) (H e i g h t)$ $=1/2(C)(Height)$
$= \frac{1}{2} (23.42) (6.76)$ $=1/2(23.42)(6.76)$
$= 79.16$ $=79.16$

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 7, 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 π3(pi)/3, the angle between sides B and C is 7π12(7pi)/12, and the length of B is 7, 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 $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 7, what is the area of the triangle?