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Work Shown:

We can apply the law of cosines

a^2 = b^2+c^2-2*b*c*cos(A)

(sqrt(5))^2 = (sqrt(2))^2+(3)^2-2*(sqrt(2))*(3)*cos(A)

5 = 2+9-6*(sqrt(2))*cos(A)

5 = 11-6*(sqrt(2))*cos(A)

11-6*(sqrt(2))*cos(A) = 5

-6*(sqrt(2))*cos(A) = 5-11

-6*(sqrt(2))*cos(A) = -6

(sqrt(2))*cos(A) = -6/(-6)

(sqrt(2))*cos(A) = 1

cos(A) = 1/(sqrt(2))

cos(A) = sqrt(2)/2

A = 45 degrees

Use the unit circle for the last step.

Interestingly, this triangle has only one angle that is a whole number. The other two angles are approximate decimal values.

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%