Find tan0 where 0 is the angle shown. Give an exact value, not a decimal approximation.

Step-by-step explanation:

We require to find the third side of the triangle.

Using Pythagoras' identity.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the third side, then

x² + 3² = 8², that is

x² + 9 = 64 ( subtract 9 from both sides )

x² = 55 ( take the square root of both sides )

x =

Thus

tanΘ = =

  tan(θ) = (3√55)/55

Step-by-step explanation:

The third side (a) of the triangle is found from the Pythagorean theorem as ...

  a^2 + b^2 = c^2

  a^2 + 3^2 = 8^2

  a^2 = 64 - 9 = 55

  a = √55

__

The mnemonic SOH CAH TOA reminds you that the tangent relation is ...

  Tan = Opposite / Adjacent

Here, the side opposite angle θ has length 3, and the side adjacent is the one we just found, √55. Then ...

  tan(θ) = 3/√55

Rationalizing the denominator by multiplying by (√55)/(√55), we find the tangent to be ...

  tan(θ) = (3/55)√55

the y will be in still but your answer will be y x 3

step-by-step explanation:

jk: )

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.