A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . What is the area of the triangle?

Question

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . What is the area of the triangle?

1 Answer

Impact of this question

1956 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-01T01:19:14

Given measurements do not obey the Greater Angle and Greater Side theorem. Hence triangle cannot be formed.

Explanation:

$a = 8, b = 7, ˆ B = \frac{π}{12}, ˆ A = \frac{2 π}{3}$ $a = 8, b = 7, hatB = pi/12, hat A = (2pi)/3$

To find area of the triangle.

![https://study.com/academy/lesson/http://inequalities-in-one-triangle.html](https://useruploads.socratic.org/Q3xXoD87R6mI6CFec7YU_greater%20side.jpg)

$As per the Greater Angle and Greater Side theorem$ $color(brown)("As per the Greater Angle and Greater Side theorem"$

$a > b since ˆ A > ˆ B$ $color(crimson)(a > b " since" hat A > hat B$

$a < b though ˆ A > ˆ B$ $color(red)(a < b " though " hat A > hat B$

Hence cannot form a triangle with the given measurements.

Science

Math

Humanities

... and beyond

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . 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. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is π12(pi)/12 and the angle between B and C is 2π3 (2pi)/3. What is the area of the triangle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{2 π}{3}$ $(2pi)/3$ . What is the area of the triangle?