Curriculum / Math / 10th Grade / Unit 4: Right Triangles and Trigonometry / Lesson 12
Math
Unit 4
10th Grade
Lesson 12 of 19
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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.
The core standards covered in this lesson
G.SRT.C.8 — Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
The foundational standards covered in this lesson
8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Brandon and Madison use different triangles to determine the slope of the line shown below.
Brandon started at (0,-1) and drew a right triangle going up 2 units and right 3 units. Madison started at (-3,-3) and drew a right triangle going up 6 units and right 9 units.
Below is a line segment on a coordinate grid.
Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a person spots a ship at an angle of depression of 20°. The lighthouse is 28 meters tall and sits on a cliff 45 meters tall as measured from sea level. What is the horizontal distance between the lighthouse and the ship?
Geometry > Module 2 > Topic E > Lesson 29 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Samuel is at the top of a tower and will ride a trolley down a zip line to a lower tower. The total vertical drop of the zip line is 40 feet. The zip line’s angle of elevation from the lower tower is 11.5°. Sam’s friend is not going to zip-line but wants to walk along the ground from the tall tower to the lower tower. How far will Sam’s friend walk to meet him?
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 11
Lesson 13
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.
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.
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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