Question

A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 2, respectively. The angle between A and C is `(11pi)/24` and the angle between B and C is `(3pi)/8`. What is the area of the triangle?

Answer 1

`A=7/2`

Explanation:

The third angle is given by
`pi-3/8*pi-11/24*pi=pi/6`
Using that
`A=1/2*a*b*sin(gamma)` we get

`A=1/2*7*2*sin(pi/6)` or

`A=7/2`

Answer 2

Hence with given measurements we cannot form a triangle.

Explanation:

`a = 7, b = 2, hat A = (3pi)/8, hat B = (11pi)/24`

Lawof sines. : a / sin A = b / sin B#

`a / sin A = 7 / sin ((3pi)/8) ~~ 7.5767`

`b / sin B = 2 / sin ((3pi)/8) ~~ 2.1648`

From the above we can see,

`a / sin A != b / sin B`

Answer 3

We cannot form a triangle with given measurements.

Explanation:

`a = 7, b = 2, hat A = (3pi)/8 = (9pi)/24, hat B = (12pi)/24`

Greater side will have greater angle opposite to it.

Since `a > b (7 > 2), hat A` must be `hat B`

But `hat A (9pi)/24 < hat B (11pi)/24`

Since the values do not satisfy the theorem, we cannot form a triangle with given measurements.