Two sides of a triangle measure 8 ft and 12 ft, respectively. The included angle is 65˚. Approximately how long is the third side of the triangle?

Approximately 11 feet.

Step-by-step explanation:

Let the length of the third side of the triangle be represented by x. Applying Cosine rule, we have:

= + - 2abCos C

⇒ = + - 2(8 x 12) Cos

       = 64 + 144 - 192 x 0.42262

       = 208 - 81.143

       = 126.857

x =

  = 11.2631

x ≅ 11

The length of the third side of the triangle is approximately 11 feet.

idk sry

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.