Answer:
4.87 ft
Step-by-step explanation:
The height of the skylight =
The height of the blue △ - the height of the red △
Let <em>b</em> ft be the height of the blue △.
sin 60° = 
<em>b</em> = 25 sin 60°
Let <em>r</em> ft be the height of the red △.
tan 40° = 
<em>r</em> = 20 tan 40°
The height of the skylight
= 25 sin 60° - 20 tan 40°
= 4.87 ft (rounded to the nearest hundredth)
Direct variation: y=kx where k is some number thats not 0
that means if x is 2, y is 2k. if x is 1, y is k. if x is 0, y is 0.
notice: no matter what k is, when you put 0 in for x, y will always be 0. that means that a direct variation always goes through the origin, a.k.a. (0,0).
do all lines go through the origin? nah. a line is y=mx+b, where m and b are some numbers. a line is only a direct variation if b is 0. this makes sense because if b is 0, then the y-intercept is 0, so the line goes through the origin.
in conclusion, no, not all linear relationships are direct varations, but all direct variations are linear relationships.
