Question

Scarlett is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 33 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 27^{\circ}
∘
, and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 33^{\circ}
∘
. If her eyes are 1.67 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.

Answer 1

The radio antennas' height is $4.6m$

From the attached diagram, the distance between point $AA$ and point $BB$distance $H-h$.

Steps on how to determine the radio antennas' height

To find the distance $H$, we make use of the relationship

$\dfrac{H}{33m}=tan33^\circ\\\\ \implies H=33m\cdot tan33^\circ$

To find the distance $h$, we make use of the relationship

$\dfrac{h}{33m}=tan27^\circ\\\\ \implies h=33m\cdot tan27^\circ$

Thus, the distance $H-h$, or the height of the radio antenna, can be found as follows

$H-h=33m\cdot tan33^\circ-33m\cdot tan27^\circ\\ =33m\cdot(tan33^\circ-tan27^\circ)\\ =33m\cdot(0.6494-0.5095)\\ =33m\cdot 0.1399\\ =4.6167m \approx 4.6m$

The antenna is $4.6m$ high

Another solved problem on angles of elevation can be found here https://brainly.com/question/12483071