Solving Right Triangles

Right-triangle methods for solving right triangles.

Lesson 4 of 53 parts Practice Flashcards

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Unknown Side

Objective: Apply unknown side.

Use sine, cosine, or tangent to determine a side from a known acute angle and side.

Worked examples

Try itA right triangle has a 30° angle and hypotenuse 8. Find the side opposite 30°.Show answer

4. sin30°=1/2, so opposite is half the hypotenuse.

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Objective: Apply unknown side.

Use sine, cosine, or tangent to determine a side from a known acute angle and side.

Worked examples

Try itA right triangle has a 30° angle and hypotenuse 8. Find the side opposite 30°.Show answer

4. sin30°=1/2, so opposite is half the hypotenuse.

Objective: Apply unknown acute angle.

Use inverse trigonometric functions to determine an acute angle from a valid side ratio.

Worked examples

Try itAn acute angle has opposite=3, adjacent=4. Approximately what is the angle in degrees?Show answer

36.87°. tan θ=3/4, so θ≈arctan(0.75)=36.87°.

Objective: Apply complementary acute angles.

The two non-right angles of a right triangle add to 90°.

Worked examples

Try itOne acute angle of a right triangle is 21°. Find the other.Show answer

69°. The two acute angles are complementary.

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