Tamara is flying in a hot air balloon. The hot air balloons is flying at an altitude of 1100 feet. The ground distance to the landing site is 1400 feet.
What is Tamara's angle of depression to the landing site?
What is the actual distance between the hot air balloon and the landing site?
If you sketch this out you will have a right triangle, I will call ABC.
A is the vertex = angle of depression
AC (side b) = base = 1400 feet
BC (side a) = leg = 1100 feet
AB (side c) = hypotenuse = distance to landing site
To find angle A (angle of depression)
tan A = a/b = 1100/1400 = 0.7857
tan A = 0.7857
arctan 0.7857 = 38.16 deg
To find C (distance to airport)
c^2 = a^2 + b^2
c^2 = 1100^2 + 1400^2
c^2 = 1,210,000 + 1,960,000
c^2 = 3,170,000
c = 1780.45 feet
1780.45/5280 feet in mile = 0.34 miles
To find Tamara's angle of depression to the landing site, we can use the concept of trigonometry. The angle of depression is defined as the angle between an imaginary horizontal line and the line of sight from an observer to a point below.
First, let's define the given information:
Altitude of the hot air balloon (height above the ground): 1100 feet
Ground distance to the landing site: 1400 feet
To find the angle of depression, we need to use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the altitude (1100 feet) and the adjacent side is the ground distance (1400 feet).
Tangent (angle of depression) = opposite side / adjacent side = 1100 / 1400
To find the actual distance between the hot air balloon and the landing site, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the altitude is the perpendicular side, the ground distance is the base, and the actual distance is the hypotenuse.
Using the Pythagorean theorem: (actual distance)^2 = (altitude)^2 + (ground distance)^2
(actual distance)^2 = (1100)^2 + (1400)^2
actual distance = square root of [(1100)^2 + (1400)^2]
To find the actual distance, you can calculate the square root of the sum of the squares of the altitude and ground distance.
Please note that this explanation assumes a right triangle formation with the hot air balloon, the landing site, and the imaginary horizontal line.