At a certain time of day, the sun causes objects to cast shadows at a 65° angle with the ground. At this time of day, a flagpole casts a shadow that is 9 feet long. How tall is the flagpole to the nearest foot?
A.4 feet
B.7 feet
С.8 feet
D.19 feet

D   19 feet

Step-by-step explanation:

Let x = height of flagpole

tan 65 = x/9

9tan 65 = x

x = 19.3 ≅ 19 ft. to the nearest foot

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is