Right Triangle Trigonometry Quiz

Right Triangle Trigonometry

• Trigonometric Functions: Defined for acute angles in a right triangle. The functions relate the sides of the triangle to the angle.
• sin θ = opp/hyp
• cos θ = adj/hyp
• tan θ = opp/adj
• csc θ = hyp/opp
• sec θ = hyp/adj
• cot θ = adj/opp Where 'opp' is the side opposite to the angle, 'adj' is the side adjacent to the angle, and 'hyp' is the hypotenuse.

Evaluating Trigonometric Functions

• Example 1: Given a right triangle with hypotenuse 4 and side adjacent to the angle θ as 3, find all six trigonometric functions of θ.

Trigonometric Functions for Special Angles

• Example 2: Find sin 45°, cos 45° and tan 45°

• Use equilateral/isosceles right triangles.

• Example 3: Find sin 60°, cos 60°, sin 30°, cos 30°

• Use 30-60-90 triangles. Values derived using a triangle with sides 1, √3, and 2.

Trigonometric Identities

• Reciprocal Identities: sin θ = 1/csc θ, cos θ = 1/sec θ, tan θ = 1/cot θ, csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ

• Quotient Identities: tan θ = sin θ/cos θ, cot θ = cos θ/sin θ

• Pythagorean Identities: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, 1 + cot² θ = csc² θ

Applying Trigonometric Identities

• Example 5: Given cos θ = 0.8, find sin θ and tan θ.
• Example 6: Given tan θ = 3, find cot θ and sec θ.

Solving Right Triangles

• Example 8: A surveyor 50 feet from a tree measures an angle of elevation to the top of 71.5°. Find the height of the tree.
• Example 9: A person is 200 yards from a river. They walk 400 yards along a path to the river's edge. Find the angle between the path and the river.
• Example 10: Find the length of a skateboard ramp with a given angle of elevation (18.4°) and length of the adjacent side (4 feet).

Test your understanding of trigonometric functions related to right triangles. This quiz covers evaluating trigonometric functions, special angles, and identities. Perfect for mastering the relationships between triangle sides and angles.