Curriculum / Math / 10th Grade / Unit 4: Right Triangles and Trigonometry / Lesson 1
Math
Unit 4
10th Grade
Lesson 1 of 19
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Define the parts of a right triangle and describe the properties of an altitude of a right triangle.
The core standards covered in this lesson
G.CO.A.1 — Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.SRT.B.4 — Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
The foundational standards covered in this lesson
8.G.A.4 — Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.B.6 — Explain a proof of the Pythagorean Theorem and its converse.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson, specifically Criteria for Success 3, connects to Unit 2, Lesson 11 because the altitude of an isosceles triangle is the perpendicular bisector.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Annotate the following diagram with the vocabulary words of “leg” and “hypotenuse.”
Given: $${\overline{BD}}$$ is the altitude of right triangle $${\triangle ABC}$$ through right angle $${\angle B}$$. Prove: $${\triangle ABD\sim \triangle BCD}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Find the measure of $${AD}$$ and $${DB}$$ given:
$${AC=16}$$
$${AB=8}$$
$${BC=12}$$
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.
Lesson 2
Topic A: Right Triangle Properties and Side-Length Relationships
G.CO.A.1 G.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.4 G.SRT.B.5
Multiply and divide radicals. Rationalize the denominator.
A.SSE.A.2 N.RN.A.2
Add and subtract radicals.
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Topic B: Right Triangle Trigonometry
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.
G.SRT.C.6
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.
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°.Â
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.6 G.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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