A person flying in an airplane 2 miles off the ground spots a car on the ground 3 miles ahead of him. What is the angle of depression of the car?
I am not quite sure how to figure this out, is there a way somebody could help me?
horizontal distance = 3
vertical distance = 2
DRAW PICTURE
tangent of angle below horizontal = 2/3 = 0.66666666.......
so angle = 33.7 deg
Ah ok thank you so much Damon, I see what my mistake was thank you so much for clarifying my mistake. Have a nice day!
You are welcome.
Yes, I can help you figure out the angle of depression of the car. The angle of depression is the angle formed between the downward line of sight from an observer and an object below the observer. In this case, the observer is the person flying in the airplane and the object is the car on the ground.
To solve this problem, we can use trigonometry, specifically the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the opposite side is the height at which the person is flying (2 miles off the ground) and the adjacent side is the horizontal distance between the person and the car (3 miles).
Here are the steps to find the angle of depression:
1. Draw a triangle representing the situation. The horizontal line represents the ground, the vertical line represents the height of the observer, and the hypotenuse represents the line of sight from the observer to the car.
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3 miles 2 miles
2. Use the tangent function. The tangent of an angle is calculated as:
tangent(angle) = (height of observer) / (horizontal distance to the car)
In this case, the tangent of the angle of depression is:
tangent(angle) = 2 miles / 3 miles
3. Solve for the angle. To find the angle, take the inverse tangent (arctangent) of the tangent calculated in the previous step:
angle = arctan(2/3)
4. Use a calculator or refer to a trigonometric table to find the inverse tangent of 2/3. The result will be in radians. If you want the answer in degrees, you can convert it by multiplying by 180 and dividing by π (pi).
That's it! You now have the method to find the angle of depression of the car when a person is flying in an airplane 2 miles off the ground and spots the car 3 miles ahead.