Question

mikayla is looking up at a flag that is 50 feet away from her at an angle of elevation from the ground level of $35^\circ$ what is the height of the flagpole (x) and the distance between mikayla and the top of the flagpole (y)? (1 point)$\bigcirc$ x = 71.41 ft. and y = 87.17 ft.$\bigcirc$ x = 61.04 ft. and y = 35.01 ft.$\bigcirc$ x = 35.01 ft. and y = 35.70 ft.$\bigcirc$ x = 35.01 ft. and y = 61.04 ft.

Explanation:

Step1: Calculate flagpole height x

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=35^\circ$, adjacent side = 50 ft, opposite side = $x$.
$\tan(35^\circ) = \frac{x}{50}$
$x = 50 \times \tan(35^\circ)$
$x \approx 50 \times 0.7002 = 35.01$ ft

Step2: Calculate distance y (hypotenuse)

We use the cosine function: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$, where hypotenuse = $y$.
$\cos(35^\circ) = \frac{50}{y}$
$y = \frac{50}{\cos(35^\circ)}$
$y \approx \frac{50}{0.8192} = 61.04$ ft

Answer:

x = 35.01 ft. and y = 61.04 ft.