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Trig Project

1.) The plane left LaGuardia Airport at 3:25 pm and, about two minutes later, struck a flock of birds. The plane had
travelled four miles from LaGuardia and was ascending at an angle of elevation of 7.7°. Calculate the plane's
height above ground level at the time of the bird strike to the nearest tenth of a foot.
The plane still climbed in altitude for 19 more seconds after the bird strike even after it lost thrust in both engines,
reaching a maximum height of 3060 ft.

2.) In order to reach its maximum height of 3060 ft., the plane had to increase its altitude by 242 ft and travel a
horizontal distance of 7150 ft.
(a) Calculate the distance the plane had to travel in order to increase its altitude by 242 ft. Round your answer
to the nearest tenth of a foot.
(b) Find the angle of elevation (to the nearest hundredth of a degree) at which the plane climbed during this
time interval. You do not have to draw a diagram to answer this part of the question.

3.) At this point, the plane started to descend. As the plane turned, its altitude dropped from 3060 feet to 1650 feet
above ground level. Calculate the angle of depression at which the plane descended to the nearest hundredth of
a degree if the horizontal distance it travelled was 0.5 miles.

4.) The plane continued to descend, but leveled off to an angle of depression of 3º.
(a) If the plane descended for two miles diagonally, how many feet (to the nearest tenth) did it drop in
b) Using the information provided in problem 3 and your answer to part (a) of problem 4, find the new
altitude of the plane at this time. Show your work.

5.) At this point, the plane crossed over the George Washington Bridge and landed in the Hudson River at an angle
of depression of 2º. From the time the plane crossed over the bridge to the time it landed in the river, it travelled
3.5 miles horizontally.
(a) By how many feet (to the nearest tenth) did the airplane descend in altitude during this time interval?
(b) Using the information from problem 4(b) and problem 5(a), find the new height of the plane (in feet) after
its descent.
(c) If the bridge is 212 feet above the water, by how many feet did the airplane clear the bridge? Show your
work.
(d) Air Traffic Control at La Guardia Airport reported seeing the aircraft pass less than 900 feet above the
George Washington Bridge. Do your calculations support this statement? Explain
​

Trig Project1 The plane left LaGuardia Airport at 3 25 pm and about two minutes later struck a flock of birds The plane hadtravelled four

Answer :

Problem 1: We can use the tangent of the angle of elevation, which is equal to the opposite side (height) over the adjacent side (distance). So,

tan(7.7°) = height / 4 miles

height = tan(7.7°) * 4 miles

height ≈ 0.53 miles or 2802 feet to the nearest tenth.

Problem 2(a): We can use Pythagorean theorem here,

horizontal distance = 7150 ft, vertical distance = 242 ft

total distance = sqrt((7150)^2 + (242)^2)

total distance ≈ 7176.3 feet to the nearest tenth.

Problem 2(b): We can use tangent again for angle of elevation,

tan(angle) = opposite/adjacent

tan(angle) = 242/7150

angle ≈ atan(242/7150)

angle ≈ 1.93° to two decimal places.

Problem 3: Using tangent for angle of depression,

horizontal distance=0.5*5280=2640 ft, vertical distance=3060-1650=1410 ft

tan(angle)=1410/2640

angle≈atan(1419/2649)

angle≈28.07° to two decimal places.

Problem 4(a): Using tangent again,

tan(3°)=height/distance

height=tan(3°)*10560 feet

height≈555 feet

Problem 4(b): Previous altitude=1659 feet Dropped altitude=555 feet New altitude=1659-555≈1104 feet

Problem 5(a): Using tangent again for this problem,

Tan(2°)=height/distance

Height=tan(2°)*18480

Height≈646.8feet

Problem 5(b): Previous altitude from problem4(b)=1104feet Dropped altitude from problem5(a)=646.8feet New altitude=1104-646.8≈457.2feet

Problem 5©: Height of the bridge=212 feet Altitude of the plane=457.2 feet Clearance=457.2-212≈245.2 feet

Problem 5(d): The calculations show that the airplane cleared the bridge by approximately 245.2 feet, which is more than 900 feet. Therefore, the statement from Air Traffic Control at LaGuardia Airport is not supported by these calculations.

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