Deshaun is looking up at a flag that is 50 feet away from him at an angle of elevation from ground level of 35°

Question

35
°
What is the flagpole’s height, x, and the distance between Deshaun and the top of the flagpole, y?(1 point)
Responses

x=35.01 ft.
𝑥
=
35.01

ft.
and y=61.04 ft.
𝑦
=
61.04

ft.
x equals 35.01 ft. and x equals 61.04 ft.

x=71.41 ft.
𝑥
=
71.41

ft.
and y=87.17 ft.
𝑦
=
87.17

ft.
x equals 71.41 ft. and x equals 87.17 ft.

x=35.01 ft.
𝑥
=
35.01

ft.
and y=35.70 ft.
𝑦
=
35.70

ft.
x equals 35.01 ft. and x equals 35.70 ft.

x=61.04 ft.
𝑥
=
61.04

ft.
and y=35.01 ft.

Answer 1

To find the height of the flagpole (x) and the distance from Deshaun to the top of the flagpole (y), we can use trigonometry.

Given:

• Distance from Deshaun to the flagpole (adjacent side in a right triangle) = 50 feet
• Angle of elevation (θ) = 35°

1. Calculating the height of the flagpole (x): We can use the tangent function, which is defined as: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Here, the opposite side is the height of the flagpole (x), and the adjacent side is the distance to the flagpole (50 feet). \[ \tan(35°) = \frac{x}{50} \] To find x: \[ x = 50 \cdot \tan(35°) \] Using a calculator: \[ \tan(35°) \approx 0.7002 \] Therefore: \[ x \approx 50 \cdot 0.7002 \approx 35.01 \text{ feet} \]

2. Calculating the distance from Deshaun to the top of the flagpole (y): We can use the hypotenuse (y) of the right triangle: \[ y = \sqrt{(50^2 + x^2)} \] We already found \(x \approx 35.01\): \[ y = \sqrt{(50^2 + (35.01)^2)} \approx \sqrt{(2500 + 1225.7001)} \approx \sqrt{3725.7001} \] Using a calculator: \[ y \approx 61.04 \text{ feet} \]

So, the height of the flagpole \(x\) is approximately 35.01 feet, and the distance from Deshaun to the top of the flagpole \(y\) is approximately 61.04 feet.

Thus, the correct response is: x=35.01 ft. and y=61.04 ft.