PPT - Angles of Elevation & Angles of Depression (G.8 ... - Free Printable

Let's analyze each of the four diagrams to identify the angles of elevation (marked with an X) and angles of depression (marked with a Y).

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🔹 Definitions:

- Angle of Elevation: The angle formed above the horizontal line when looking up at an object.
- Angle of Depression: The angle formed below the horizontal line when looking down at an object.

These angles are always measured from the horizontal.

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## 🟦 Diagram 1 (Top Left)

- A person at point H looks up at a kite at point J.
- A dashed horizontal line is drawn from H to the kite’s height.
- The triangle is HJK, with right angle at K.

✔ Angle of elevation: The angle between the horizontal line from H and the line of sight to the kite (HJ).
➡️ This is ∠JHK → Mark with X

✔ Angle of depression: There is no downward view here; the person is looking up.
So, no angle of depression in this diagram.
→ Leave blank or write "none"

> ✔ Answer:
> ∠ of elevation: X at ∠JHK
> ∠ of depression: None

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## 🟨 Diagram 2 (Top Right)

- A person in a tower at point T looks down at a fire at point F.
- A horizontal dashed line goes from T to A.
- The line of sight is from T to F.

✔ Angle of depression: The angle below the horizontal from T to F → this is ∠ATF
→ Mark with Y

✔ Angle of elevation: From the fire (F) looking up to T, it would be ∠TFB — but we’re usually measuring from the observer’s eye level.
Since the observer is at T, and they're looking down, there is no angle of elevation from their perspective.

> ✔ Answer:
> ∠ of elevation: None
> ∠ of depression: Y at ∠ATF

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## 🟩 Diagram 3 (Bottom Left)

- An airplane at point F above water.
- A boat at point E on water.
- A horizontal dashed line from F to H.
- Line of sight from E to F.

✔ Angle of elevation: From the boat (E) looking up to the plane (F) → this is ∠FEG
→ Mark with X

✔ Angle of depression: From the plane (F) looking down to the boat (E) → this is ∠HFE
→ Mark with Y

> ✔ Answer:
> ∠ of elevation: X at ∠FEG
> ∠ of depression: Y at ∠HFE

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## 🟪 Diagram 4 (Bottom Right)

- A person sitting at point S on a cliff.
- Looking down at point U on the ground.
- Horizontal dashed line from S to T.
- Line of sight from S to U.

✔ Angle of depression: From S, looking down to U → this is ∠TSU
→ Mark with Y

✔ Angle of elevation: From U looking up to S → this is ∠SUT
→ Mark with X

> ✔ Answer:
> ∠ of elevation: X at ∠SUT
> ∠ of depression: Y at ∠TSU

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✔ Final Answers:

#### Diagram 1:
- ∠ of elevation: X at ∠JHK
- ∠ of depression: None

#### Diagram 2:
- ∠ of elevation: None
- ∠ of depression: Y at ∠ATF

#### Diagram 3:
- ∠ of elevation: X at ∠FEG
- ∠ of depression: Y at ∠HFE

#### Diagram 4:
- ∠ of elevation: X at ∠SUT
- ∠ of depression: Y at ∠TSU

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💡 Summary:

- Always look for the horizontal line from the observer.
- Elevation: Upward angle → X
- Depression: Downward angle → Y
- The same angle (in measure) often appears as both elevation and depression due to alternate interior angles (when lines are parallel), but we label based on observer's position.

Let me know if you'd like a labeled version!