ABC Is An Isosceles Triangle. What Is The Height Of The Triangle When The Known Lengths Are 10cm And 13cm?

by ADMIN 107 views

=====================================================

Introduction

In geometry, an isosceles triangle is a triangle with two sides of equal length. When dealing with isosceles triangles, we often need to find the height of the triangle, which is the perpendicular distance from the vertex opposite the base to the base itself. In this article, we will explore how to find the height of an isosceles triangle when the known lengths are 10cm and 13cm.

Understanding Isosceles Triangles

An isosceles triangle has two sides of equal length, which are called the legs of the triangle. The third side, which is opposite the vertex where the two equal sides meet, is called the base of the triangle. The height of the triangle is the perpendicular distance from the vertex opposite the base to the base itself.

Properties of Isosceles Triangles

Isosceles triangles have several important properties that can be used to find the height of the triangle. One of the most important properties is that the altitude of an isosceles triangle bisects the base and the vertex angle. This means that the altitude divides the base into two equal segments and the vertex angle into two equal angles.

Finding the Height of an Isosceles Triangle

To find the height of an isosceles triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In the case of an isosceles triangle, we can draw an altitude from the vertex opposite the base to the base itself, which creates two right triangles.

Using the Pythagorean Theorem

Let's assume that the length of the base of the isosceles triangle is 10cm and the length of the equal sides is 13cm. We can draw an altitude from the vertex opposite the base to the base itself, which creates two right triangles. The length of the altitude is the height of the triangle, which we want to find.

Using the Pythagorean theorem, we can write:

  • a^2 + b^2 = c^2

where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

In this case, a is the length of the base of the isosceles triangle, which is 10cm, and b is the length of the altitude, which we want to find. c is the length of the equal side of the isosceles triangle, which is 13cm.

Plugging in the values, we get:

  • 10^2 + b^2 = 13^2

Simplifying the equation, we get:

  • 100 + b^2 = 169

Subtracting 100 from both sides, we get:

  • b^2 = 69

Taking the square root of both sides, we get:

  • b = √69

Simplifying the expression, we get:

  • b = 8.30cm

Therefore, the height of the isosceles triangle is approximately 8.30cm.

Conclusion

In this article, we explored how to find the height of an isosceles triangle when the known lengths are 10cm and 13cm. We used the Pythagorean theorem to find the height of the triangle, which is the perpendicular distance from the vertex opposite the base to the base itself. The height of the isosceles triangle is approximately 8.30cm.

Future Work

In the future, we can explore other properties of isosceles triangles and how to use them to find the height of the triangle. We can also explore other types of triangles and how to find their heights.

References

Glossary

  • Isosceles Triangle: A triangle with two sides of equal length.
  • Height: The perpendicular distance from the vertex opposite the base to the base itself.
  • Pythagorean Theorem: A theorem that states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

=====================================================

Introduction

In our previous article, we explored how to find the height of an isosceles triangle when the known lengths are 10cm and 13cm. In this article, we will answer some frequently asked questions about isosceles triangles.

Q: What is an isosceles triangle?

A: An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called the legs of the triangle, and the third side, which is opposite the vertex where the two equal sides meet, is called the base of the triangle.

Q: What are the properties of an isosceles triangle?

A: Isosceles triangles have several important properties that can be used to find the height of the triangle. One of the most important properties is that the altitude of an isosceles triangle bisects the base and the vertex angle. This means that the altitude divides the base into two equal segments and the vertex angle into two equal angles.

Q: How do I find the height of an isosceles triangle?

A: To find the height of an isosceles triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In the case of an isosceles triangle, you can draw an altitude from the vertex opposite the base to the base itself, which creates two right triangles.

Q: What is the Pythagorean theorem?

A: The Pythagorean theorem is a theorem that states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. It can be written as:

  • a^2 + b^2 = c^2

where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

Q: How do I use the Pythagorean theorem to find the height of an isosceles triangle?

A: To use the Pythagorean theorem to find the height of an isosceles triangle, you need to draw an altitude from the vertex opposite the base to the base itself, which creates two right triangles. Then, you can use the Pythagorean theorem to find the length of the altitude, which is the height of the triangle.

Q: What are some real-world applications of isosceles triangles?

A: Isosceles triangles have many real-world applications, including:

  • Architecture: Isosceles triangles are used in the design of buildings and bridges to provide structural support and stability.
  • Engineering: Isosceles triangles are used in the design of machines and mechanisms to provide balance and stability.
  • Art: Isosceles triangles are used in the creation of art and design to provide balance and harmony.

Q: What are some common mistakes to avoid when working with isosceles triangles?

A: Some common mistakes to avoid when working with isosceles triangles include:

  • Confusing the base and the legs: Make sure to identify the base and the legs of the triangle correctly.
  • Using the wrong formula: Make sure to use the correct formula to find the height of the triangle.
  • Not drawing the altitude: Make sure to draw the altitude from the vertex opposite the base to the base itself.

Conclusion

In this article, we answered some frequently asked questions about isosceles triangles. We hope that this article has provided you with a better understanding of isosceles triangles and how to use them in real-world applications.

Glossary

  • Isosceles Triangle: A triangle with two sides of equal length.
  • Height: The perpendicular distance from the vertex opposite the base to the base itself.
  • Pythagorean Theorem: A theorem that states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

References