An airplane pilot over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from th
e airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?
2 answers:
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Answer: approximately 5148 feet directly north of point A
This is equivalent to 0.975 miles
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Explanation:
Check out figure 1 (attached image below) to see how the drawing is set up.
Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.
Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.
The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.
Note that triangle ABC is a right triangle. The 90 degree angle is at point A.
We can use the pythagorean theorem to solve for x
See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.
This means the sound wave takes about 4.68 seconds to go from point C to point A.
With this x value, we can compute the expression 1100x to get
1100*x = 1100*4.68 = 5,148 feet
To convert this to miles, divide by 5280
(5148)/(5280) = 0.975
Therefore,
5148 feet = 0.975 miles
"of" means multiply and "is" means equal
1. x = 14
x = 14(3) <em>multiply both sides by 3 to isolate "x"</em>
x = 42
2. x = 14
x = 14(5) <em>multiply both sides by 5 to isolate "x"</em>
x = 70
3. x = 14
2x = 14(5) <em>multiply both sides by 5 </em>
2x = 70
x = 35 <em>divide both sides by 2 to isolate "x"</em>
4. x = 14
7x = 14(8) <em>multiply both sides by 8 </em>
7x = 112
x = 16 <em>divide both sides by 7 to isolate "x"</em>
Answers: 42, 70, 35, 16