Find all solutions for a triangle with a=40 degrees , b=60 degrees and c = 20.

A = 40 degrees

B = 60 degrees

C = 80 degrees

a = 13.1

b = 17.6

c = 20

Step-by-step explanation:

They give us A = 40 degrees and B = 60 degrees and in one triangle the sum of the angles should be 180, so you add 40 and 60, and then subtract that value by 180.

40 + 60 = 100

180 - 100 = 80

C = 80 degrees

From here you use the law of sines

20/sin(80) = a/sin(40)

when you cross multiply them you should get this:

20 * sin(40) = sin(80)*a

Simplify them

12.9 = sin(80) * a

Divide them to isolate the variable

12.9/sin(80) = a

a = 13.1

To find side length b you use law of sines again

20/sin(80) = b/sin(60)

Cross multiply

20 * sin(60) = sin(80) * b

Simplify

17.3 = sin(80) * b

Divide to isolate the variable

17.3/sin(80) = b

b = 17.6

40 +60+20= 120

Step-by-step explanation:

25

Step-by-step explanation:

A perfect square is the product of a rational number multiplied by itself.

If rewrite the given numbers in the prime factorization form, we get

We can see there is onl;y 25 a number which can be written as the product of a rational number multiplied by itself i. e.5.

Therefore, 25 is a perfect square.