Curriculum / Math / 10th Grade / Unit 4: Right Triangles and Trigonometry / Lesson 6
Math
Unit 4
10th Grade
Lesson 6 of 19
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Lesson Notes
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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.
The core standards covered in this lesson
G.SRT.C.6 — Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
The foundational standards covered in this lesson
G.CO.C.10 — Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Below is a set of similar right triangles. Find the ratio of the side lengths within each triangle that describe the side opposite the marked angle divided by the hypotenuse.
What is the sine of 0°, 45°, 60°, and 90°?
$${\triangle ABC}$$ is a right triangle. What is the sine of $${\angle BAC}$$?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Explain how you know that the following statement is always, sometimes, or never true:
“You can find the sine of any angle in any triangle by finding the ratio of the length of the opposite side over the length of the hypotenuse.”
Find the sine of each angle shown in the diagram below. Then, predict between which two benchmark angle measures the angles fall between based on the sine.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
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.
Topic A: Right Triangle Properties and Side-Length Relationships
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
Define and prove the Pythagorean theorem. Use the Pythagorean theorem and its converse in the solution of problems.
G.SRT.B.4
Define the relationship between side lengths of special right triangles.
G.SRT.B.4G.SRT.B.5
Multiply and divide radicals. Rationalize the denominator.
A.SSE.A.2N.RN.A.2
Add and subtract radicals.
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Topic B: Right Triangle Trigonometry
G.SRT.C.6
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°.
G.SRT.C.7
Describe and calculate tangent in right triangles. Describe how the value of tangent changes as the angle measure approaches 0°, 45°, and 90°.
G.SRT.C.6G.SRT.C.7
Solve for missing sides of a right triangle given the length of one side and measure of one angle.
G.SRT.C.8
Topic C: Applications of Right Triangle Trigonometry
Find the angle measure given two sides using inverse trigonometric functions.
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.
Solve a modeling problem using trigonometry.
Topic D: The Unit Circle
Define angles in standard position and use them to build the first quadrant of the unit circle.
F.TF.A.2
Use the first quadrant of the unit circle to define sine, cosine, and tangent values outside the first quadrant.
Topic E: Trigonometric Ratios in Non-Right Triangles
Derive the area formula for any triangle in terms of sine.
G.SRT.D.9
Verify algebraically and find missing measures using the Law of Sines.
G.SRT.D.10
Verify algebraically and find missing measures using the Law of Cosines.
Use side and angle relationships in right and non-right triangles to solve application problems.
G.SRT.D.11
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