# An airplane is approaching an airport at an altitude of 300 feet.Looking directly downt eh runway, the pilot sights an angle of depression with a measure of 29 degrees to the near end of the...

An airplane is approaching an airport at an altitude of 300 feet.Looking directly downt eh runway, the pilot sights an angle of depression with a measure of 29 degrees to the near end of the runways, and one with a measure of 7 to the far end of the runway. Find the length of the runway?

http://www.ursulinestl.org/class_files/13/3072/25668.pdf this is the diagram .

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### 1 Answer

Please see the attached figure for a representation of the situation.

<LHF=<HFG= 7 degrees (opposite interior angles)

Similarly, <LHN=<HNG = 29 degrees (opposite interior angles)

Now consider `Delta HFG, tan 7^o=300/(GF)=300/(GN+FN)` --- (i)

Again from `Delta HNG, tan 29^o=300/(GN)` --- (ii)

`rArr GN=300/tan29^o`

From (i), `300/(tan29^o)+FN = 300/(tan7^o)`

`rArr FN=300/(tan7^o)-300/(tan29^o)`

`=300(1/(tan7^o)-1/(tan29^o))`

`=300*6.3403=1902 feet`

**Therefore, length of the runway was 1902 ft.**