Topicmab9d270e20add82d_1528449000663_0Topic

Solving right triangles

Levelmab9d270e20add82d_1528449084556_0Level

Third

Core curriculummab9d270e20add82d_1528449076687_0Core curriculum

VII. Trigonometry. The student:

6) calculates the angles of the triangle and the length of its sides with the corresponding data (solves the triangles).

Timingmab9d270e20add82d_1528449068082_0Timing

45 minutes

General objectivemab9d270e20add82d_1528449523725_0General objective

Interpreting and manipulating information presented in both mathematical and popular science texts, as well as in the form of graphs, diagrams, tables.

Specific objectivesmab9d270e20add82d_1528449552113_0Specific objectives

1. Communicating in English, developing mathematics, scientific, technical and IT competences, developing learning skills.

2. Calculation of the lengths of segments and measures of angles in right triangles.

Learning outcomesmab9d270e20add82d_1528450430307_0Learning outcomes

The student:

- student calculates the lengths of segments and measures of angles in right triangles.

Methodsmab9d270e20add82d_1528449534267_0Methods

1. Aquarium.

2. Competition.

3. Case study.

Forms of workmab9d270e20add82d_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmab9d270e20add82d_1528450127855_0Introduction

Students work using the „fish in the aquarium” method. They are divided in two groups. The first group of students sits in a circle and discuss the trigonometric functionstrigonometric functionstrigonometric functions. The second group of students are the observers. They analyze their colleagues’ conversation in terms of the selection of the terms of each trigonometric function and the relationship between these functions.

The teacher acts as a mentor. He or she verifies students' statements and explains all doubts.

Proceduremab9d270e20add82d_1528446435040_0Procedure

The teacher informs students that the aim of the lesson is to solve right triangles.

Discussion - What does it mean to solve a rectangular triangle? Students make hypotheses, check them and formulate conclusions.

Conclusion:

- To solve the right triangle means to calculate the length of its sides and the measure of its angles.

Task
Students working in groups analyze the material presented in the interactive show. They make hypotheses. They formulate all the necessary conclusions.

[Slideshow]

Conclusion:

- In order to determine the length of the sides of a right‑angled triangle and the measures of its acute angles, we use trigonometric functions and the Pythagorean theorem.mab9d270e20add82d_1527752256679_0- In order to determine the length of the sides of a right‑angled triangle and the measures of its acute angles, we use trigonometric functions and the Pythagorean theorem.

Using the information learned, the students independently solve the tasks.

Task
Take part in the competition. You can get 3 points for each exercise. Students who score the most points will receive very good grades.

Competition task

1. Solve the right triangle whose side lengths are 8 cm and 6 cm.

2. In a right‑angled triangle, the hypotenuse is 18 cm long and one of the sides is 10 cm long. Calculate the length of the other leg and the measure of the sharp angles.

3. The length of the hypotenuse of the right triangle is equal 25 cm, and one of the sharp angles has a measure of 40°. Calculate the lengths of the legs.

4. The length of the leg opposite the angle of 54° is equal 4 cm. Calculate the length of the other legs of this triangle.

5. Solve the right triangle if the length of the hypotenuse is 24 cm and the leg length is 20 cm.

After the competition, the teacher summarizes the results, explains the doubts and assesses students’ work.

An extra task:
The isosceles trapeziumisosceles trapeziumisosceles trapezium has bases of the length of 12 dm and 20 dm, and its perimeter is 64 dm. Calculate the angles of this trapezium.

Lesson summarymab9d270e20add82d_1528450119332_0Lesson summary

After solving all the tasks, the students do the revision exercises.

Together, they formulate conclusions to remember.

- To solve the right triangle means to calculate the length of its sides and the measure of its angles.

- In order to determine the length of the sides of a right‑angled triangleright‑angled triangleright‑angled triangle and the measures of its acute angles, we use trigonometric functionstrigonometric functionstrigonometric functions and the Pythagorean theorem.

Selected words and expressions used in the lesson plan

acute angleacute angleacute angle

hypotenusehypotenusehypotenuse

isosceles trapeziumisosceles trapeziumisosceles trapezium

leglegleg

rhombusrhombusrhombus

right‑angled triangleright‑angled triangleright‑angled triangle

solving right‑angled trianglessolving right‑angled trianglessolving right‑angled triangles

trigonometric functionstrigonometric functionstrigonometric functions