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Calculating the Height of an Isosceles Triangle

Understanding Isosceles Triangles

An isosceles triangle is a triangle with two equal sides and two equal angles. The height of an isosceles triangle is the perpendicular distance from the vertex opposite the base to the base.

Formula for Height of an Isosceles Triangle

The height of an isosceles triangle can be calculated using the following formula: ``` h = √(s<sup>2</sup> - (b/2)<sup>2</sup>) ``` where: * h is the height of the triangle * s is the length of one of the equal sides * b is the length of the base

Step-by-Step Calculation

To calculate the height of an isosceles triangle, follow these steps: 1. Measure the length of one of the equal sides, labeled as "s". 2. Measure the length of the base, labeled as "b". 3. Substitute the values of "s" and "b" into the formula: h = √(s² - (b/2)²). 4. Calculate the square of "s" and subtract half of the square of "b" from it. 5. Take the square root of the result to obtain the height of the triangle.

Example

Consider an isosceles triangle with equal sides of length 5 cm and a base of length 6 cm. Using the formula, we can calculate the height as follows: ``` h = √(5<sup>2</sup> - (6/2)<sup>2</sup>) h = √(25 - 9) h = √16 h = 4 cm ``` Therefore, the height of the isosceles triangle is 4 cm.

Applications of Isosceles Triangle Height

The height of an isosceles triangle is useful in various applications, such as: * **Calculating the area:** The area of an isosceles triangle is given by the formula A = (1/2) * b * h. * **Finding the centroid:** The centroid of an isosceles triangle is located at a distance of h/3 from the base. * **Analyzing geometric shapes:** The height of an isosceles triangle helps in understanding the properties and relationships within geometric figures.

Conclusion

Calculating the height of an isosceles triangle is a fundamental concept in geometry. By applying the formula and following the steps outlined above, you can accurately determine the height of an isosceles triangle for various applications in mathematics and engineering.

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