A PERSON STANDING 30 FEET FROM A FLAGPOLE CAN SEE THE TOP OF THE POLE AT A 35 DEGREE ANGLE OF ELEVATION. THE PERSON'S EYE LEVEL IS 5 FEET FROM THE GROUND. FIND THE HEIGHT OF THE FLAGPOLE TO THE NEAREST FOOT.

26.01 ft

21 feet

To find the height of the flagpole, we can use trigonometry. Let's denote the height of the flagpole as 'x'.

First, let's draw a diagram to better understand the problem. The diagram will consist of a right triangle formed by the person, the flagpole, and the line connecting the person's eye level to the top of the flagpole.

In the right triangle, we have:

- The side opposite to the angle of elevation, which is the height of the flagpole (x).
- The side adjacent to the angle of elevation, which is the distance from the person to the flagpole (30 feet).
- The hypotenuse, which is the line connecting the person's eye level to the top of the flagpole.

So, we can use the trigonometric function tangent (tan) to find the height of the flagpole:

tan(angle) = opposite / adjacent

In this case, we are given the angle of elevation (35 degrees) and the adjacent side (30 feet).

tan(35 degrees) = x / 30

To find the value of x, we can rearrange the equation:

x = 30 * tan(35 degrees)

Using a calculator, the approximate value of x is 20.20.

However, this value represents the total height of the flagpole from the ground to the top. Since the person's eye level is 5 feet from the ground, we need to subtract this height to find the height of the flagpole from the ground to the base.

Height of the flagpole = Total height - Eye level height
Height of the flagpole = 20.20 feet - 5 feet
Height of the flagpole = 15.20 feet

Therefore, the height of the flagpole is approximately 15 feet.