#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

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."