Question

myesha is trying to find the height of a radio antenna on the roof of a local building. she stands at a horizontal distance of 13 meters from the building. the angle of elevation from her eyes to the roof (point $a$) is $29^{\circ}$, and the angle of elevation from her eyes to the top of the antenna (point $b$) is $43^{\circ}$. if her eyes are 1.51 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.

Explanation:

Step1: Define height from eyes to A

Let $h_A$ = height from eyes to A. Use tangent:
$\tan(29^\circ) = \frac{h_A}{13}$

Step2: Calculate $h_A$

$h_A = 13 \times \tan(29^\circ) \approx 13 \times 0.5543 = 7.2059$

Step3: Define height from eyes to B

Let $h_B$ = height from eyes to B. Use tangent:
$\tan(43^\circ) = \frac{h_B}{13}$

Step4: Calculate $h_B$

$h_B = 13 \times \tan(43^\circ) \approx 13 \times 0.9325 = 12.1225$

Step5: Find antenna height

Antenna height = $h_B - h_A$
$12.1225 - 7.2059 \approx 4.9166 \approx 5$

Answer:

5 meters