You are about to run up a set of 100 stairs. The diagonal distance up the 100 stairs is 62.5 feet and the angle of elevation from the base of the stairs to the top is
31
62.5 ft.
h
31°
What is the height difference from where you start to where you finish?
Round your answer to the nearest hundredth.
h=
feet

h = 32.2 ft

Step-by-step explanation:

Since we have a right triangle, to get the value of h, we will have to use the appropriate trigonometric ratio

From the diagram given, h faces the angle and that makes it the opposite side

62.5 ft faces the right angle and that makes it the hypotenuse

The trigonometric ratio that connects the two is the sine

thus, we have it that;

sine 31 = h/62.5

h = 62.5 * sin 31

h = 32.2 ft

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

25% is the answer