JHS2 Mathematics · Term 3, Week 4

Measurement

Lesson notes

Learning Objectives

Indicator: B8.3.2.1.5 - Establish the relationship between the basic trigonometric ratios and solve problems involving right-angled triangles.

By the end of the lesson, learners can:

Identify the opposite, adjacent and hypotenuse sides of a right-angled triangle relative to a given angle.
Define the three primary trigonometric ratios: sine, cosine and tangent, as ratios of pairs of sides.
Compute the value of sin X, cos X and tan X for a given angle in a right-angled triangle using side lengths.
Explain the meaning of angle of elevation and angle of depression in real-life situations.
Apply trigonometric ratios together with the Pythagoras theorem to solve problems involving right-angled triangles, including angles of elevation and depression.

Curriculum details

Strand: Geometry and Measurement (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: B8.3.2.1 - Apply the Pythagoras theorem, the primary trigonometric ratios and the formulas for determining the area of a circle to solve real problems.
Indicator: B8.3.2.1.5 - Establish the relationship between the basic trigonometric ratios and solve problems involving right-angled triangles.
Suggested placement: Term 3, Week 4 (Week 28 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 145
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g.1 Identify and recognise the three primary trigonometric ratios.
i. Establish the sine, cosine and tangent of an angle in a right-angled triangle

Wide colour mathematical teaching visual is organised as a worked calculation with horizontal divisions, coloured... — A wide colour mathematical teaching visual is organised as a worked calculation with horizontal divisions, coloured regions, open white space around the main marks. Visible labels, values, and notation include: B; a; Opposite; sine of LA = sin A = Hypotenuse; =; Adjacent; cosine of LA = cos A =; Hypotenuse; tangentof LA = tan A =.

i. Find sin X, cos X and tan X in the diagram

Nearly square black-and-white mathematical teaching visual is organised as a table with horizontal divisions,... — A nearly square black-and-white mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions, open white space around the main marks. The nearly square black-and-white table is arranged with horizontal divisions, vertical divisions, open white space around the main marks.

ii. Write two trig ratios of the angle marked θ in the diagram below:

E.g. 2 Explain the angles of elevation and depression in real life situations.

Nearly square colour mathematical teaching visual is organised as a table with horizontal divisions, vertical... — A nearly square colour mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions, coloured regions. Visible labels, values, and notation include: ongle of; norizontol; angle; depression.

Wide colour mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions,... — A wide colour mathematical teaching visual is organised as a table with horizontal divisions, vertical divisions, coloured regions. The wide colour table is arranged with horizontal divisions, vertical divisions, coloured regions.

E.g.3 Use trig ratios and the Pythagoras theorem to solve problems involving angles of elevation and depression.
i. A hunter, on top of a tower, sees a fire at an angle of depression of 30˚. The height of the tower is 18m. What is the distance between the fire and the hunter? Round off your answer to 2 significant figures.

Fire-observation diagram forms a right triangle from a 1.8 metre vertical tower, the horizontal ground to a fire at... — A fire-observation diagram forms a right triangle from a 1.8 metre vertical tower, the horizontal ground to a fire at F, and a downward line of sight making a 30-degree angle with a dashed horizontal through the observer. The wide colour table is arranged with horizontal divisions, vertical divisions, coloured regions.

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