Question

Joanna knows that when her line of sight is 34 ft to the top of a flagpole, the angle of elevation is 27 degrees, and her eyes are 5 ft from the ground. What should be the height of the flagpole?

Answer 1

By using the tangent of the 27 degrees angle, we can calculate that the height of the flagpole is approximately 22.323 feet when considering the 5-ft eye level of the observer.

Step-by-step explanation:

To find the height of the flagpole, we can use trigonometric ratios. Specifically, Joanna is using the tangent ratio since she is given an angle of elevation and the distance from her eye to the top of the flagpole. The tangent of an angle in a right triangle is the ratio of the opposite side (height of flagpole minus Joanna's eye level) to the adjacent side (Joanna's distance to the flagpole).

In this case, the tangent of 27 degrees is equal to the height of the flagpole (we'll call it 'h') minus Joanna's eye level (5 ft) divided by her distance from the pole (34 ft). We can set up the equation as follows:

tan(27 degrees) = (h - 5 ft) / 34 ft

By solving for 'h', we can give Joanna the height of the flagpole:

• h - 5 ft = 34 ft × tan(27 degrees)
• h = 34 ft × tan(27 degrees) + 5 ft
• h ≈ 34 ft × 0.5095 + 5 ft
• h ≈ 17.323 + 5 ft
• h ≈ 22.323 ft

Therefore, the height of the flagpole is approximately 22.323 feet.