How to Find the Height of a Triangle

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  • 0:00 Finding the Height of…
  • 1:18 Area Method
  • 2:00 Pythagorean Theorem Method
  • 4:00 Lesson Summary
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Lesson Transcript
Instructor: Kimberly Osborn
A triangle can be described using a variety of its characteristics, from its area, legs, hypotenuse, height, etc. This lesson will focus on the height of a triangle and two methods that can be used to solve when it is unknown.

Finding the Height of a Triangle

Back when I was in my first year of college and I thought I wanted to become an architect, I was assigned the task of recreating a scale drawing of the Great Pyramid of Khufu. Sounds simple enough, right? Unfortunately there was a small catch: all I was given was an image of the pyramid with the area and sides labeled for one of its faces. That's it. How was I supposed to make a scale drawing when I didn't have any of the pyramid's dimensions? More importantly, how was I supposed to draw the pyramid without its height? This is when I realized the true nature of the assignment. My teacher didn't want us to just make a drawing, he wanted us to use math to find our dimensions and THEN make the drawing. Sneaky right?

After careful research, I learned of two methods that can be used to find the height of a triangle. Since each face on the pyramid is an isosceles triangle, we are going to focus on the face specifically and not the entire image of the pyramid.

The two methods that we will be using in this lesson are the area method and the Pythagorean Theorem method.

It's important to note the area method works for ALL triangles, while the Pythagorean Theorem method only works on equilateral, isosceles, or right triangles. It does NOT work on irregular triangles.

Area Method

Before we can begin using the area method, we must first remember the area formula of a triangle:

Area Formula

Now we can simply take the area provided for the triangle and the length of its base and plug these numbers into our formula to set up an equation. In this case, our missing height is labeled h. We get:

Area formula with numbers plugged in

Using our steps to solve for the missing variable in an equation, we get:

Work for area formula

Pythagorean Theorem Method

Let's say you aren't given the height of your triangle, but you are working with an isosceles or equilateral triangle and you are given the measure for the sides of your triangle. You can then use the Pythagorean Theorem method.

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