Question

A man standing near a radio station antenna observes that the angle of elevation to the top of the antenna is 64 He then walks 68 feet further away and observes that the angle of elevation to the top of the antenna is 43 Find the height of the antenna to the nearest foot.

Answer 1

The height of the radio station antenna is approximately 116 feet to the nearest foot.

From the diagram in the attached image

$h=\text{the height of the radio station antenna}\\x=\text{the distance from the foot of the radio station antenna to where the man stood at first}$

we now have the following relationships

$tan64^\circ=\frac{h}{x}\\\\\implies x=\frac{h}{tan64^\circ}$

and

$tan43^\circ=\frac{h}{68+x}\\\\\implies x=\frac{h}{tan43^\circ}-68$

we can equate the two relationships to eliminate $x$.

$\frac{h}{tan64^\circ}=\frac{h}{tan43^\circ}-68$

solving for the height of the radio station antenna, $h$, we get

$h=\frac{68\times tan43^\circ \times tan64^\circ}{tan64^\circ -tan43^\circ}\approx 116ft\text{ (to the nearest foot)}$

Learn more about angle of elevation here: brainly.com/question/12483071