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 $\frac{5 π}{12}$ $(5pi)/12$ , 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 $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{5 π}{12}$ $(5pi)/12$ , and the length of B is 2, what is the area of the triangle?

1 Answer

Impact of this question

1418 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-10T11:51:44

Area of the triangle is $2.36 (2 d p)$ $2.36(2dp)$ sq units

Explanation:

The angle between sides A and B is $∠ C = \frac{π}{3} = \frac{180}{3} = 60^{0}$ $/_C=pi/3 = 180/3 = 60^0$
The angle between sides B and C is $∠ A = \frac{5 π}{12} = \frac{5 \cdot 180}{12} = 75^{0}$ $/_A= (5pi)/12 = (5*180)/12= 75^0$
The angle between sides C and A is $∠ B = 180 - (60 + 75) = 45^{0}$ $/_B=180-(60+75) = 45^0$
$B = 2$ $B=2$ (given) Applying sine law we get $\frac{A}{sin A} = \frac{B}{sin B} or A = 2 \cdot \frac{sin 75}{sin 45} = 2.73$ $A/sinA=B/sinB or A=2*sin75/sin45=2.73$ Now $A = 2.73; B = 2$ $A=2.73 ; B=2$ and their included angle $∠ C = 60^{0}$ $/_C=60^0$ So area of the triangle is $a \cdot b \cdot \frac{sin C}{2} = 2.73 \cdot 2 \cdot \frac{sin 60}{2} = 2.36 (2 d p)$ $a*b*sinC/2= 2.73*2*sin60/2=2.36(2dp)$ sq units [Ans}

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 $\frac{5 π}{12}$ $(5pi)/12$ , 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 (pi)/3π3(pi)/3, the angle between sides B and C is (5pi)/125π12(5pi)/12, 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 $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{5 π}{12}$ $(5pi)/12$ , and the length of B is 2, what is the area of the triangle?