Question

A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 7, respectively. The angle between A and C is `(pi)/12` and the angle between B and C is `(pi)/6`. What is the area of the triangle?

Answer 1

Kindly check whether the question is correct?

Also, it is sufficient if you know only one side, as we already have three angles known.

Explanation:

Kindly check whether the question is correct?
Smaller side will have smaller angle opposite to it and bigger side wall have bigger angle opposite to it.

In the given sum, side A is 2 and `/_A is pi / 6, and side B is 7 and /_B is pi/6`.

Also, it is sufficient if you know only one side, as we already have three angles known.

Answer 2

Area of the #Delta ABC = 1120.0834

Explanation:

Assumption : only side B given as 7.

Three angles are `/_A = pi/6, /_B = pi/12, /_C = (3pi)/ 4`

`A / sin (pi/6) = 7 / sin (pi/12) = C / sin ((3pi) / 4)`

`A = (7*sin (pi/6)) / sin (pi/12) = **13.523**`

`C = (7 * sin ((3pi)/4))/ sin (pi/12) = **19.1244**`

Semi perimeter `s =( A + B + C ) /2 = (13.523 + 7 + 19.1244) / 2 = **19.8237**`

`s - A = 19.8237 - 13.523 = 6.3007`
`s - B = 19.8237 - 7 = 12.8237`
`s - C = 19.8237 - 19.1244 = 0.6993`

Area of `Delta ABC = sqrt (s (s-A) (s-B) (s - C))`
`= sqrt( 19.8237 * 6.3007 * 12.8237 * 0.6993) = **1120.0834**`