Question

standing 200ft from the base of an antenna, Maria measures the angle of elevation to the top of the antenna to be 38 degrees. If her eye level is 5ft above the ground, what is the height of the antenna to the nearest foot?

Answer 1

Given: The bearing and distance of Maria and an antenna

To Determine: The height of the antenna from the given information

Solution

From the given information, the diagram below can be deduced

From the diagram above, the height of the antenna is TB

Using SOH CAH TOA

`\begin{gathered} tan38^0=(TC)/(EC) \\ EC=BG=200ft \\ SO, \\ tan38^0=(TC)/(200) \\ TC=200* tan38^0 \end{gathered}`
`\begin{gathered} TC=156.257ft \\ TB=TC+CB \\ EG=CB=5ft \\ TB=156.257+5 \\ TB=161.257ft \\ TB\approx161ft \end{gathered}`

Hence, the height of the antenna is 161ft