Question

Jason is standing 100 feet from the base of a flag pole. He is looking up to the top of the pole at an angle of 30°. If his eye level is 5.5 feet, how tall is the flagpole? 100 ft 30° 5.5 ft​

Answer 1

Explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle with the flagpole as the vertical side, the horizontal distance from Jason to the flagpole as the adjacent side, and the line of sight from Jason's eye to the top of the flagpole as the hypotenuse.

Since Jason is looking up at a 30° angle, we know that the opposite side of this triangle is (flagpole height) and the hypotenuse is (distance from Jason to the pole + Jason's eye level), which is 100 + 5.5 = 105.5 feet.

Now we can use the tangent function:

tan(30°) = opposite/adjacent

tan(30°) = height/100

height = 100 * tan(30°)

height = 57.74 feet (rounded to two decimal places)

Therefore, the flagpole is approximately 57.74 feet tall.