Applications of Trigonometry

Right-triangle methods for applications of trigonometry.

Lesson 5 of 53 parts Practice Flashcards

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Angle of Elevation

Objective: Apply angle of elevation.

Angle of elevation is measured above a horizontal line of sight.

Worked examples

Try itA line of sight rises 4 units over a horizontal run of 4 units. What is its angle of elevation?Show answer

45°. Rise equals run, so tan θ=1 and θ=45°.

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Objective: Apply angle of elevation.

Angle of elevation is measured above a horizontal line of sight.

Worked examples

Try itA line of sight rises 4 units over a horizontal run of 4 units. What is its angle of elevation?Show answer

45°. Rise equals run, so tan θ=1 and θ=45°.

Objective: Apply angle of depression.

Angle of depression is measured below a horizontal line of sight.

Worked examples

Try itA line of sight drops 5 units over a horizontal run of 5 units. What is its angle of depression?Show answer

45°. Vertical drop equals horizontal run, so the acute angle is 45°.

Objective: Apply modeling distances.

Draw a right triangle and identify the known and unknown parts before choosing a ratio.

Worked examples

Try itA right-triangle model has horizontal run 4 and vertical rise 3. Which ratio finds the angle at the ground?Show answer

tan θ = 3/4. Opposite over adjacent is 3i/4i=3/4.

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