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In the section Solving 8th-grade math problems on pages 94, 95, 96, 97 of the Kite Wings book volume 1 - Exercise 1: Pythagorean theorem, Mytour will guide students on how to calculate and compare the area of a square based on the Pythagorean theorem, inviting students to refer to it.
Solving 8th-grade Math Kite Wings Volume 1 pages 94, 95, 96, 97
Exercise 1: Pythagorean theorem
Solving 8th-grade Math Kite Wings Volume 1 page 96
Solving Exercise 1 - Kite Wings 8th Grade Volume 1 page 96
Problem:
Given right triangle ABC at A. Find the length of the remaining side in each of the following cases:
a) AB = 8 cm, BC = 17 cm
b) AB = 20 cm, AC = 21 cm
c) AB = AC = 6 cm.
Solution method:
Applying the Pythagorean theorem
Answer:
2. Solving Exercise 2 - Kite Wings 8th Grade Volume 1 page 96
Problem:
Is the triangle formed by the lengths of three sides in each of the following cases a right triangle or not?
a) 12 cm, 35 cm, 37 cm
b) 10 cm, 7 cm, 8 cm
c) 11 cm, 6 cm, 7 cm
To solve:
Apply the inverse Pythagorean theorem
The answer is:
Solving 8th-grade Math Kite Wings Volume 1 page 97
Solving Exercise 3 - Kite Wings 8th Grade Volume 1 page 97
Problem:
Given an isosceles right triangle with the length of the right angle side equal to 1 dm. Calculate the length of the hypotenuse of that triangle.
Solution method:
Applying the Pythagorean theorem
Answer:
The length of the hypotenuse of the triangle is:
4. Solve Exercise 4 - Kite Wings 8th Grade Volume 1 page 97
Problem:
Given an equilateral triangle with side length a.
a) Calculate the length of the altitude of that triangle in terms of a.
b) Calculate the area of that triangle in terms of a.
Method:
Applying the Pythagorean theorem
Answer:
a) Calculate the length of the altitude of that triangle in terms of a:
b) Calculate the area of that triangle in terms of a:
5. Solve exercise 5 - Kite Wings 8th Grade Volume 1 page 97
Problem:
Figure 9 describes a wooden stick 3.5 meters long leaning against a vertical wall. The foot of the wooden stick is 2.1 meters away from the wall. How far is the point where the wooden stick touches the wall from the ground?
Solution method:
Applying the Pythagorean theorem
Answer:
The distance from the point where the wooden stick touches the wall to the ground is:
6. Solving Exercise 6 - Kite Wings 8th Grade Volume 1 page 97
Problem:
Figure 10 depicts a cross-section of an outdoor stage with a canopy. The height of the front frame is about 7 m, the height of the back frame is 6 m, and the frames are 5 m apart. What is the length of the stage canopy (rounded to the nearest hundredth)?
Solution method:
Applying the Pythagorean theorem
Answer:
Let BC be the length of the stage canopy.
Then, we have:
Here is the guide to solving 8th-grade math problems on pages 94, 95, 96, 97 of the Kite Wings volume 1 Pythagorean theorem. To prepare for the next lesson, you can preview the solution for 8th-grade math problems on pages 98, 99, 100 of the Kite Wings volume 1 - Exercise 2: Quadrilaterals. Additionally, the practical activities and experiences on pages 92, 93 of the Kite Wings volume 1 - Topic 2 will help reinforce the knowledge you have learned. You can review the answers here. Wish you good luck with your math studies.
Refer to other 8th-grade math materials:
- 8th-grade Math Kite Wings
- Solving 8th-grade math problems on pages 59, 60, 61, 62 of the CTST volume 1- Exercise 1: Pythagorean theorem
