You approach a hill on top of which there is a tall radio antenna. You know from your map that your horizontal distance from the bottom of the radio antenna is 600 feet. The angle of elevation to the bottom of the antenna is 10∘, and the angle of elevation to the top of the antenna is 25∘.

The length of the antenna is 174 feet.

Step-by-step explanation:

Given that the horizontal distance from the bottom of the radio aAntenna is 600 feet.

The angle of elevation to the bottom of the antenna is 10∘, and the angle of elevation to the top of the antenna is 25∘.

Let AB is the hill, BC is the antenna on the top of the hill, and point O is the viewer's eye as shown in the figure.

OA=600 feet

The length of the antenna = BC

From the figure, BC=AC-AB...(i)

Now in triangle AOB, we have

feet ...(ii)

Similarly, in triangle AOC, we have

feet ...(iii)

By applying the values from equation (ii) and (iii) in the equation (i), we have,

BC=279.8-105.8=174 feet

Hence, the length of the antenna is 174 feet.

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