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## Trigonometry

### Course: Trigonometry>Unit 1

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 start text, start color #11accd, a, n, g, l, e, space, o, f, space, e, l, e, v, a, t, i, o, n, end color #11accd, end text between the horizontal and your line of sight to the object.
A solid, horizontal line. A point on the line is labeled you. A dashed arrow up to the right to a point labeled object.
A solid, horizontal line. A point on the line is labeled you. A dashed arrow up to the right to a point labeled object. The dashed arrow is labeled sight line. The inside angle made from the horizontal line and the dashed arrow is labeled angle of elevation.
Similarly, when you see an object below you, there's an start text, start color #e07d10, a, n, g, l, e, space, o, f, space, d, e, p, r, e, s, s, i, o, n, end color #e07d10, end text between the horizontal and your line of sight to the object.
A solid, horizontal line. A point on the line is labeled you. A dashed arrow down to the right to a point labeled object.
A solid, horizontal line. A point on the line is labeled you. A dashed arrow down to the right to a point labeled object. The dashed arrow is labeled sight line. The inside angle made from the horizontal line and the dashed arrow is labeled angle of depression.

## Practice problem

The image below is a model of Aya, point A, looking up to Super Girl, point S, in the sky.
A rectangle where the base is the shorter side and the height is the longer side. Point A is on the bottom left corner of the rectangle. Point S is in the top right corner of the rectangle. Line segment A S is a diagonal for the rectangle. The bottom angle created by cutting angle A with line segment A S is labeled one. The top angle created by cutting angle A with line segment A S is labeled two. The top angle created by cutting angle S with line segment A S is labeled three. The bottom angle created by cutting angle S with line segment A S is labeled four.
What is the angle of elevation from Aya to Super Girl?

What is the angle of depression from Super girl to Aya?

## 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?
• Unless you are trying to code or take engineering as a career you likely won't come in contact with it.
• 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.
• 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.
• Can someone please explain this better?
• 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 :)
• how do you find angle of elevation if side measures are given but no degree given?
• You can use the inverses of SIN, COS, and TAN, (arcsin, arccos, and arctan) to calculate a degree from given side lengths.
• 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.
• 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.
• will angle 1 be equal to angle 3
• Yes, they will be equal if the "sky line" and the "ground line" are parallel lines.
• If I'm not trying to be an engineer what other situation would I ever need to know about this
• Probably never – just like you would never need to know about tectonic plates, or that Paris is the capital of France, or that boxing is a sport.
In fact, there are people in the world right now who never spent a single minute in school and still live their lives.

Then again, who knows what could have become of those people if they had had the chance to go to school and learn the same nonsense that you are learning right now?