A search and rescue plane flying at an altitude of 1000 feet spots a ship in the ocean with an angle of depression of 7 degrees. The pilot follows his line of site and flies directly toward the boat for 0.7 miles. At this point his altitude is _____ feet. Use 1 mile = 5280 feet, and round to the nearest whole number. (Here, the pilot is descending along the hypotenuse of the original triangle. He travels 0.7 miles along this hypotenuse. Answer the question by finding the height of the new triangle.)
sin7o = 1000/L
L=1000/sin7 = 8206 Ft=Line of site(hyp)
L' = 8206 - 0.7*5280 = 4510 Ft.
h = 4510*sin7 = 550 Ft.
To find the altitude at the new point, we can use trigonometry and the given information.
First, let's draw a diagram to help visualize the problem:
|\
| \
altitude | \ 7°
of plane |___\
0.7 miles
We are given the angle of depression, which is the angle between the line of sight from the plane to the ship and the horizontal line. In this case, the angle of depression is 7 degrees.
Since the plane flies directly toward the boat for 0.7 miles, we can consider this distance as the base of the triangle formed by the altitude and the line of sight.
Now, we can use the tangent function to solve for the altitude:
tan(7°) = altitude / 0.7 miles
Rearranging the equation to solve for the altitude, we get:
altitude = tan(7°) * 0.7 miles
Now, let's convert the 0.7 miles to feet:
1 mile = 5280 feet
So, 0.7 miles = 0.7 * 5280 feet = 3696 feet (rounded to the nearest whole number).
Now, let's calculate the altitude:
altitude = tan(7°) * 3696 feet
Using a calculator, we find:
altitude ≈ 455.77 feet (rounded to the nearest whole number)
Therefore, at the point 0.7 miles toward the ship, the pilot's altitude is approximately 456 feet.