SAMPLE LESSON: MATHEMATICS
Class: Form 5
Title of Module: Plane Geometry
Title of Chapter: Trigonometry
Title of Lesson: Angle of Elevation, Angle of
Depression
Duration of Lesson: 50mins
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Trigonometry Lesson: Angle of Elevation and Angle of Depression in Plane Geometry, Study notes of Mathematics
A mathematics lesson plan for Form 5 students on the topic of Trigonometry, specifically focusing on Angle of Elevation and Angle of Depression. The lesson includes objectives, prerequisite knowledge, motivation, examples, and application exercises. Students will learn how to find angles and distances using trigonometric ratios.
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2021/2022
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SAMPLE LESSON: MATHEMATICS
Class: Form 5
Title of Module : Plane Geometry Title of Chapter: Trigonometry Title of Lesson: Angle of Elevation, Angle of Depression Duration of Lesson: 50 mins
MATHEMATICS LESSON
CLASS : Form 5; Duration : 50 minutes TOPIC : Plane Geometry Lesson : Trigonometry Lesson Objectives: At the end of the lesson, you should be able to:
- Translate a given situation into a Mathematical figure; - Find angle of Elevation; - Find angle of Depression; -. Find length of a distance Prerequisite knowledge: You can do the following:
- Use Pythagoras theorem to solve a right triangle;
- Use appropriate trigonometric ratio to find lengths of sides and measures of angles in a triangle If not go back and revise these notions. Motivation : Practical applications of trigonometry by Engineers, Surveyors, Pilot and Navigators frequently involve measure of angles of elevation and depression based on the given situation. Angles of elevation and depression are often used in trigonometry word problems. Every time you look up at something in the sky, you are creating something called the Angle of Elevation with your eyes and when you look down at something on the ground, you are creating an angle called Angle of Depression. Didactic Materials:
- Ruler, Pencil, calculator, References:
- GEOMETRY, Eugene D. Nicholas, Mervine L. Edwards, E Henry Garland, Sylvia, A Hoffman, Albert Mamary, William F Palmer (1991), Holt, Rinehart and Winston, Inc.
- https://www.mathsteacher.com.au/year10/ch15_trigonometry/12_elevation_depression/23elevdep.htm
- https://www.bbc.co.uk/bi tesize/guides/z98jtv4/revision/
- The length of the altitude to the base of an isosceles triangle is 16m. The measure of a base angle is 55o. Find the length of the base of the triangle to the nearest meter.
- Find the length indicated as x on the diagram below. Answers: 1) x = 24.0m; 2) xo^ = 54o; 3) The length of the base = 22.4m; 4) x = 21. NB: If you have any of them wrong, go back and revise the notions before you continue the lesson.
Angle of Elevation Angle of Depression
Examples:
The height of the tree is BC. A man standing at a distance AC from the see will have to lift up his eyes to see the top of the tree. The angle through which he takes up his eyes, is the angle of elevation
The diagram below summaries In the diagram above, angle labelled 1 indicates the angles of elevation. It is the angle by which the ground observerโs line of vision must be raised or elevated with respect to the horizontal, to sight an object at B. While the angle labelled 2 is the angle of depression. It is the angle by which an observer at Bโs line of vision must lowered or depressed, with respect to the horizontal to sight an object at A.
Examples:
- From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34ยบ. How far is the object from the base of the cliff? Let x m be the distance of the object from the base of the cliff. Angle of depression = 34o But ๐ด๐๐ ฬ = ๐ต๐๐ฬ because they are alternate angles โด ๐ด๐ ฬ ๐ = 34 ๐ From triangle APO, we have: ๐ก๐๐ 34 ๐^ = 40 ๐ฅ โด ๐ฅ๐ก๐๐ 340 = 40 ๐ฅ ร x โน 0. 6745 ๐ฅ = 40 โด ๐ฅ = 59. 30
- You are on a trip through a desert. At a distance d , you can see mountains, and quick measurement tells you that the angle between the mountain top and the ground is 13.4o. You know that the highest point (the centre) of the mountain is 2500m high. How far away are you from the centre of the mountain?
b. The figure in a) is a right triangle. One of the trigonometric ratios can be used to find the ground distance. On the diagram the length of the ground distance FG is the side adjacent to angle 27 o^ while the side PG with distance of 900m is the opposite side. tan 27 = ๐๐บ ๐บ๐น
900 ๐บ๐น (Your calculator should give you Tan 27^0 = 0.5095 to 4decimal places) โด ๐บ๐น = 900 ร 0. 5095 = 1766. 4 ๐ ๐ป๐๐ ๐ฎ๐๐๐๐๐ ๐ ๐๐๐๐๐๐๐ = ๐๐๐๐๐
- A tree 50m high casts a 35m shadow. Find, to the nearest degree, the measure of the angle of elevation of the sun.
Solution: The situation can be represented by the figure by the side. From the figure, and using trigonometric ratios, ๐ก๐๐๐ด = 50 35 โน ๐ก๐๐๐ด = 1. 4285 โน< ๐ด = ๐ก๐๐โ^11. 4285 โด ๐๐๐๐๐ ๐๐ ๐๐๐๐ฃ๐๐ก๐๐๐ ๐๐ ๐กโ๐ ๐ ๐ข๐ โ 55 ๐ Points to remember The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight). The angle of elevation of the object from the observer is ๐ผ If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression.
- You are standing 10 meters away from a tree. The angle of elevation from your eyes to the top of the tree is 65o. Find how far away you are from the tree given that the distance from your feet to your eyes is 1.6m tall.