12-14 please in detail

Step-by-step explanation:

12) looking at the right angle triangle,

x = hypotenuse

y = adjacent side

Opposite side = 4

To determine x, we would apply

the sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 30 = 4/x

x = 4/sin30 = 4/0.5

x = 8

To determine y, we would apply

the Cosine trigonometric ratio.

Cos θ, = adjacent side/hypotenuse. Therefore,

Cos 30 = y/8

y = 8Cos30 = 8 × 0.866

y = 6.93

14) looking at the right angle triangle,

hypotenuse = 22

y = opposite side

x = adjacent side

To determine y, we would apply

the sine trigonometric ratio.

Therefore,

Sin 45 = y/22

y = 22Sin45 = 22 × 0.7071

y = 15.6

x = y = 15.6 because the triangle is an isosceles triangle.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

the answer is 8/21

hope this