A triangle have two sides are known 20m & 30m respectively.find third side where area is 430 square meter.there have different angle .

use law of cosines to get the included angle t.

Then 20*30*sin(t) = 430

actually, it's 1/2 that.

To find the third side of a triangle where two sides are known and the area is given, you can use the formula for the area of a triangle:

Area = (1/2) * base * height

In this case, the two known sides are 20m and 30m, and you have the area as 430 square meters. However, it is not mentioned which side is the base and which side is the height. Since the triangle has different angles, one of the known sides can be considered as the base, and the other side will be the height.

Let's consider the side of 30m as the base and the side of 20m as the height:

Area = (1/2) * base * height
430 = (1/2) * 30 * 20

Simplifying the equation:

430 = 300

This equation is not possible since 430 is not equal to 300.

Now let's consider the side of 20m as the base and the side of 30m as the height:

Area = (1/2) * base * height
430 = (1/2) * 20 * 30

Simplifying the equation:

430 = 300

Again, this equation is not possible since 430 is not equal to 300.

Based on the information provided, it is not possible to find the third side of the triangle where the area is 430 square meters and the two known sides are 20m and 30m, given that there are different angles.