What is the angle of elevation?

The angle of elevation is the angle formed between the horizontal baseline and the observer's upward line of sight when looking at an object above.

What is the angle of depression?

The angle of depression is the angle formed between the horizontal line of sight and the observer's downward look when observing an object below.

Are the angles of elevation and depression related?

Yes. If an observer at the ground looks up at a tower, the angle of elevation is equal to the angle of depression of an observer at the tower looking down, because they form alternate interior angles between parallel horizontal lines.

Angle of ELEVATION - Real-World Right Triangle Solver

Horizontal Distance (d)40 m

Calculated Height (h)≈ 23.09 m

Line of Sight (L)≈ 46.19 m

Variable Adjuster

Observer Distance (d)40m

1580

Angle (θ)30°

1575

Auto-Sweep Engine

Target Param:

Sweep Speed: 2x

Angle of Elevation

TRIG

Angle of elevation is measured looking upwards from a horizontal line to an object above.

\begin{aligned}\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}} \\ h = d \tan\theta\end{aligned}

Whiteboard Solver Steps

Step 1

Identify Triangle Sides

We model the scenario as a right-angled triangle where: - The horizontal distance along the ground is the Adjacent side ( $d = 40$ m). - The height of the object is the Opposite side ( $h$ ). - The angle of elevation is the angle between the horizontal line and the line of sight ( $\theta = 30^\circ$ ).

\begin{aligned}\text{Adjacent (Distance } d\text{)} = 40\text{ m} \\ \theta = 30^\circ\end{aligned}

Step 2

Apply Tangent Function to Find Height

Since we know the adjacent side and need the opposite side, we use the tangent trigonometric ratio: $\tan\theta = \text{opposite}/\text{adjacent}$ . Multiplying the distance by the tangent of the angle gives the height: $h \approx 23.09$ meters.

\begin{aligned}\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{d} \\ h = d \times \tan\theta = 40 \times \tan(30^\circ) \approx 23.09\text{ m}\end{aligned}

Step 3

Calculate Line of Sight (Hypotenuse)

The direct line of sight from the observer to the target is the hypotenuse ( $L$ ). Using cosine ( $\cos\theta = \text{adjacent}/\text{hypotenuse}$ ), we calculate the line of sight distance: $L \approx 46.19$ meters.

L = \frac{d}{\cos\theta} = \frac{40}{\cos(30^\circ)} \approx 46.19\text{ m}

RV Anveshana