Question

xochitl is trying to find the height of a radio antenna on the roof of a local building. she stands at a horizontal distance of 12 meters from the building. the angle of elevation from her eyes to the roof (point a) is $42^\circ$, and the angle of elevation from her eyes to the top of the antenna ( point b) is $50^\circ$. if her eyes are 1.58 meters from the ground, find the height of the antenna (the distance from point a to point b). round your answer to the nearest meter if necessary.
answer attempt 1 out of 2
meters submit answer

Explanation:

Step1: Define variables for heights

Let $h_A$ = height from eyes to roof (A), $h_B$ = height from eyes to antenna top (B). Horizontal distance $d=12$ m.

Step2: Calculate $h_A$ using tangent

$\tan(42^\circ)=\frac{h_A}{d}$
$h_A = 12 \times \tan(42^\circ) \approx 12 \times 0.9004 = 10.8048$ m

Step3: Calculate $h_B$ using tangent

$\tan(50^\circ)=\frac{h_B}{d}$
$h_B = 12 \times \tan(50^\circ) \approx 12 \times 1.1918 = 14.3016$ m

Step4: Find antenna height ($h_B - h_A$)

Antenna height = $14.3016 - 10.8048 = 3.4968$ m

Step5: Round to nearest meter

$3.4968 \approx 3$ m

Answer:

3 meters