Triangle ABC has an area of 25√3/2 cm²,c=60•, a=5cm
find the angle of A and B

The possible solutions for the triangle ABC are:

(, and ):

,

(, and )

,

Step-by-step explanation:

The area of the triangle ABC is determined by the following equation:

Where:

- Area of the triangle, measured in square centimeters.

- Semiperimeter of the triangle, measured in centimeters.

, , - Sides of the triangle, measured in centimeters.

Now, we simplify the equation:

If we know that , and , the equation is simplified:

The roots of the fourth-grade polynomial are:

, , , .

Only the first two roots are physically reasonable. Then, there are only two solutions for the triangle ABC:

,

The angles A and B can be found by Law of Cosine:

Where:

, - Angles opossed to sides and , measured in sexagesimal degrees.

There are two possibilities:

(, and )

(, and )

The possible solutions for the triangle ABC are:

(, and ):

,

(, and )

,

40 is the final : )