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### Course: Get ready for AP® Calculus > Unit 4

Lesson 6: Modeling with right triangles# Angles of elevation and depression

Learn what the terms angle of elevation and angle of depression mean. The words may be big but their meaning is pretty basic!

When you see an object above you, there's an ${\text{angle of elevation}}$ between the horizontal and your line of sight to the object.

Similarly, when you see an object below you, there's an ${\text{angle of depression}}$ between the horizontal and your line of sight to the object.

## Practice problem

The image below is a model of Aya, point $A$ , looking up to Super Girl, point $S$ , in the sky.

## When are these terms useful?

Angles of elevation and depression are often used in trigonometry word problems, so it's good to know their meanings.

## Want to join the conversation?

- when can you use these terms in real life?(44 votes)
- Unless you are trying to code or take engineering as a career you likely won't come in contact with it.(63 votes)

- Hey Guys,

I'm doing math and I'm really stuck on a question. It is:

Emma is 90m due west of Michele on a level road. Emma sees the angle of elevation of the kite flown by RIley at 30 degrees, while Michele sees that it is due north at an angle of elevation of 38 degrees. What is the height of the kite?

I've tried drawing 3D models, 2D traingles etc, but I still can't solve it. I will scan and attach my working out really soon.(30 votes)- from Emma's perspective it creates a nice 30-60-90 triangle with leg opposite the 60 degree is 90 meters so the leg opposite 30 degrees is 30sqt(3) m up, and Michelle's perspective we got the angles but we don't know how high or low she is; just that she is 8 degrees more down. and that doesn't create a right tringle if we add it or create a semi circle. if they're standing in the same road level and Michelles is a few inches less than Emma then the kite it's 30sqrt(3) meters which is around 52 meters, good for a kite.(17 votes)

- Can someone please explain this better?(5 votes)
- Well basically, if your looking at something diagonally above you, you form a "sight line". The angle that would form if it was a real line to the ground is an angle of elevation.

Exact opposite if your looking diagonally down; the angle between the "sight line" and the horizon or sky is the angle of depression. Elevation for elevate, Depression for down is how I remember it.

Hope this actually helped instead of confused you more :)(39 votes)

- what is the point of trigonometry in real life. it's just people coming up with more confusing math for absolutely no reason at all.(4 votes)
- GPS uses trig, Rocket launches and space exploration uses trig, surveyors use trig. So every time you try to get to somewhere, remember that trig is helping you get there.(41 votes)

- how do you find angle of elevation if side measures are given but no degree given?(7 votes)
- You can use the inverses of SIN, COS, and TAN, (arcsin, arccos, and arctan) to calculate a degree from given side lengths.(18 votes)

- This is high school level math? Looks a bit too simple...

But the term could be useful in other word problems, so...(11 votes)- It’s going to be used in word problems and what not. As a result of that, Khan is telling us what the vocab means so we understand better.(3 votes)

- what is the pythagorean theorem?(5 votes)
- that is a great question! I love the pythagorean theorem... it is a^2 + b^2 = c^2(20 votes)

- "What is the angle of depression from Super girl to Aya?" why is it 3 and not 4?(5 votes)
- Note the definition of angle of depression again:

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line.

The angle that satisfies this definition is ∠3. ∠4 is the angle between the**vertical**line and the observation of the object, which isn't classified as an angle of depression.(6 votes)

- will angle 1 be equal to angle 3(4 votes)
- Yes, they will be equal if the "sky line" and the "ground line" are parallel lines.(7 votes)

- can someone plzz explaine this better(0 votes)
- Angles of elevation and depression are always in reference to a horizontal. Angles of elevation go up from the horizontal, thus we often use the ground as the horizontal and talk about the angle to the top of a tree or building or bird in the sky, etc. Angles of depression are slightly less visual because these are often "imaginary" horizontal lines somewhere in the sky, and the angle goes down from that horizontal. We can talk about a bird in the air seeing a mouse at some angle of depression or about trying to land a plane. With either elevation (looking up) or depression (looking down) many things would be perpendicular to the ground and/or these imaginary lines in the air, and thus create a right triangle as well as two parallel lines and a transversal (since both are hoizontal, they have to be parallel). Mostly, we talk about the vertical leg being perpendicular to the ground which means the angle of elevation will be one of the angles of the right triangle. The angle of depression would be a alternate interior angle of the parallel lines, thus these two should be equal to each other. With all this, we are ready to solve some problems mostly using trig or special right triangles.(14 votes)