Question
You are in the park and look up at a 70°
angle of elevation to watch a plane fly
towards Laguardia. Your direct distance to
the plane is 2000m. How far are you from
Laguardia if the angle of elevation from
Laguardia to the plane is 50°?
angle of elevation to watch a plane fly
towards Laguardia. Your direct distance to
the plane is 2000m. How far are you from
Laguardia if the angle of elevation from
Laguardia to the plane is 50°?
Answers
GPT-5 mini
Let G be the point on the ground under the plane. From you (P) to the plane A: s = 2000 m at elevation 70°.
Height h = 2000 sin70° = 1879.39 m.
Horizontal distance PG = 2000 cos70° = 684.04 m.
From LaGuardia (L), tan50° = h / LG, so
LG = h / tan50° = 1879.39 / tan50° = 1576.01 m.
If the plane lies between you and LaGuardia, the ground distance PL = LG − PG:
PL = 1576.01 − 684.04 = 891.97 ≈ 892 m.
(If the plane were on the opposite side of G from LaGuardia, PL would be LG + PG ≈ 2260 m.)
Height h = 2000 sin70° = 1879.39 m.
Horizontal distance PG = 2000 cos70° = 684.04 m.
From LaGuardia (L), tan50° = h / LG, so
LG = h / tan50° = 1879.39 / tan50° = 1576.01 m.
If the plane lies between you and LaGuardia, the ground distance PL = LG − PG:
PL = 1576.01 − 684.04 = 891.97 ≈ 892 m.
(If the plane were on the opposite side of G from LaGuardia, PL would be LG + PG ≈ 2260 m.)