#7 find the missing side length UM. round answer to nearest tenth.

Step-by-step explanation:

Considering the given triangle LUM, to determine UM, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

UM/SinL = UL/SinL = ML/SinU

Therefore

UM/Sin 37 = 27/Sin 108

Cross multiplying, it becomes

UMSin108 = 27Sin37

0.951UM = 27 × 0.602

0.951UM = 16.254

UM = 16.254/0.951

UM = 17.1 ft

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: