Lesson 16 | Right Triangles and Trigonometry | 10th Grade Mathematics

Objective

Derive the area formula for any triangle in terms of sine.

Lesson Map

Topic A: Right Triangle Properties and Side-Length Relationships

Lesson

Define the parts of a right triangle and describe the properties of an altitude of a right triangle.

Standards

G.CO.A.1G.SRT.B.4

Lesson

Define and prove the Pythagorean theorem. Use the Pythagorean theorem and its converse in the solution of problems.

Standards

G.SRT.B.4

Lesson

Define the relationship between side lengths of special right triangles.

Standards

G.SRT.B.4G.SRT.B.5

Lesson

Multiply and divide radicals. Rationalize the denominator.

Standards

A.SSE.A.2N.RN.A.2

Lesson

Add and subtract radicals.

Standards

A.SSE.A.2N.RN.A.2

Topic B: Right Triangle Trigonometry

Lesson

Define and calculate the sine of angles in right triangles. Use similarity criteria to generalize the definition of sine to all angles of the same measure.

Standards

G.SRT.C.6

Lesson

Define and calculate the cosine of angles in right triangles. Use similarity criteria to generalize the definition of cosine to all angles of the same measure.

Standards

G.SRT.C.6

Lesson

Derive the relationship between sine and cosine of complementary angles in right triangles, and describe sine and cosine as angle measures approach 0°, 30°, 45°, 60°, and 90°.

Standards

G.SRT.C.7

Lesson

Describe and calculate tangent in right triangles. Describe how the value of tangent changes as the angle measure approaches 0°, 45°, and 90°.

Standards

G.SRT.C.6G.SRT.C.7

Lesson

Solve for missing sides of a right triangle given the length of one side and measure of one angle.

Standards

G.SRT.C.8

Topic C: Applications of Right Triangle Trigonometry

Lesson

Find the angle measure given two sides using inverse trigonometric functions.

Standards

G.SRT.C.8

Lesson

Describe the relationship between slope and the tangent ratio of the angle of elevation/depression. Use the tangent ratio of the angle of elevation or depression to solve real-world problems.

Standards

G.SRT.C.8

Lesson

Solve a modeling problem using trigonometry.

Standards

G.SRT.C.8

Topic D: The Unit Circle

Lesson

Define angles in standard position and use them to build the first quadrant of the unit circle.

Standards

F.TF.A.2

Lesson

Use the first quadrant of the unit circle to define sine, cosine, and tangent values outside the first quadrant.

Standards

F.TF.A.2

Topic E: Trigonometric Ratios in Non-Right Triangles

Lesson

Derive the area formula for any triangle in terms of sine.

Standards

G.SRT.D.9

Lesson

Verify algebraically and find missing measures using the Law of Sines.

Standards

G.SRT.D.10

Lesson

Verify algebraically and find missing measures using the Law of Cosines.

Standards

G.SRT.D.10

Lesson

Use side and angle relationships in right and non-right triangles to solve application problems.

Standards

G.SRT.D.11

Right Triangles and Trigonometry

Objective

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Right Triangles and Trigonometry

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