A person in an airplane sights a car on the ground at an angle of depression of 40 degrees. The sight distance from the plane to the car is 2700 ft. Find the altitude of the airplane to the nearest foot.
a.2068 ft
b.2266 ft
c.4200 ft
d.1736 ft
2007-07-20 04:50:28 · 6 answers · asked by confused 3 in Science & Mathematics ➔ Mathematics
♣ a.
is it your Granny’s picture?
2007-07-20 07:04:58 · answer #1 · answered by Anonymous · 1⤊ 0⤋
The answer is d. To arrive at the answer you can use trigonometry. Draw a right triangle with the plane at one end of the hypotenuse and the car at the other. The length of the hypotenuse is known to be 2700 feet (i.e. the sight distance). The angle of depression (i.e. the angle that the hypotenuse would make with the horizontal) is 40degrees. Therefore you can find the altitude of the plane (or either missing side of this right triangle) which is the vertical leg of the right triangle that has been so drawn. That is
sin(40degres)= h/2700
h=2700sin(40degrees) = 1735.526feet
To the nearest foot then the answer is D 1736 ft
2007-07-20 05:10:45 · answer #2 · answered by sigmazee196 2 · 0⤊ 0⤋
altitude =sine 40 degree x 2700 ft = 1736 ft
answer is d. 1736 ft
2007-07-20 05:06:33 · answer #3 · answered by Anonymous · 0⤊ 0⤋
2700 * cos 50 = 1736
2007-07-20 05:05:32 · answer #4 · answered by 037 G 6 · 0⤊ 0⤋
sin(40) = height/2700
height = sin(40) * 2700 = 1736 ft
2007-07-20 05:04:42 · answer #5 · answered by civil_av8r 7 · 0⤊ 0⤋
all you have to so is apply the law of sines after you draw the picture. And then solve for x. So you get:
sin90/2700=sin50/x
xsin90=2700sin50
x=2700sin50/sin90
x=2068
2007-07-20 05:10:17 · answer #6 · answered by sweetiepie031286 1 · 0⤊ 0⤋