Need doing this question, show steps as well so i can understand it.

Explanation:

The reference angle is angle S = 41 degrees. The side opposite that (RT) is unknown and what we want to find. The adjacent side to the reference angle is TS which is 8 units long.

RT = x

TS = 8

The ratio of the opposite and adjacent side is equal to the tangent of the reference angle, so,

tan(angle) = opposite/adjacent

tan(41) = x/8

We are given the value of tan(41) to be approximately 0.869, which means we will replace "tan(41)" with this decimal value and then isolate x by multiplying both sides by 8. This happens in the section below.

tan(41) = x/8

0.869 = x/8

8*0.869 = 8*x/8

6.952 = x

x = 6.952

x = 6.95

RT = 6.95

- "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."

ok thats very interesting