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What Is an Obtuse Triangle? - Definition & Area Formula

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  • 0:05 What is an Obtuse Angle?
  • 0:50 What is an Obtuse Triangle?
  • 1:09 Finding the Area of an…
  • 2:13 More Practice
  • 4:07 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll review what an obtuse angle is and find out how it makes obtuse triangles unique. You'll also discover the formula for the area of an obtuse triangle. Then, you can test your knowledge with a brief quiz.

What Is an Obtuse Angle?

To define obtuse triangles, it will be handy to first define obtuse angles. Obtuse angles are simply angles larger than 90 degrees. We can spot them because they extend past a right angle.

Imagine tilting a car seat back so that you can lie down comfortably. You'll push it past the upright position, closer to lying flat. Where the seat's bottom and back meet would be an obtuse angle because you've pushed the back beyond a 90 degree angle.

An Obtuse Angle Goes Beyond 90 Degrees

The dashed line indicates a right angle. The seat's back is clearly pushed beyond that point, forming an obtuse angle. Obtuse angles don't have to be that dramatic, however. As long as the angle measures over 90 degrees, it's obtuse.

As long as the angle is larger than 90 degrees it is obtuse.

Although this angle barely goes beyond 90 degrees, it's still obtuse by definition.

What Is an Obtuse Triangle?

An obtuse triangle is any triangle that contains an obtuse angle. Here are some examples:

a triangle with an indicated angle greater than 90 degrees
a triangle with an indicated angle greater than 90 degrees

Both triangles are obtuse because they contain an angle greater than 90 degrees. No matter where in the triangle that angle is, as long as it's greater than 90 degrees, the triangle containing it is obtuse.

Finding the Area of an Obtuse Triangle

Farmer John has a triangular piece of land he wants to seed with cotton. He's drawn this diagram of the land:

diagram of an obtuse triangular field with length 50 feet and height 80 feet

How will he find out how much area he'll need to seed?

The formula for the area of an obtuse triangle is:

A = 1/2 (b * h)

where b is the length of the triangle's base and h is the triangle's height.

We can choose any side of the triangle to be the base. To find the height, we extend a perpendicular line from the base to the opposite vertex. Sometimes, the perpendicular line will lie outside the triangle. In that case, we can extend a line from the base so we can draw the height.

obtuse triangle with height indicated

In Farmer John's case, his field is an obtuse triangle. Its base is 50 feet long and he indicated that its height is 80 feet. We can plug these values into our formula for the area of an obtuse triangle:

A = 1/2 (b * h)
A = 1/2 (50 * 80)
A = 1/2 * 4,000
A = 2,000

The area of the field Farmer John will need to seed with cotton is 2,000 square feet.

More Practice

Let's find the area of a couple more obtuse triangles.

Bobby and Mary want to make a huge kite. They've agreed to each buy half of the needed material. The kite they plan to make will be 8 feet across and 16 feet high. How much material will Mary need to buy?

Well, the kite will be a diamond 8 feet across. But Mary's only responsible for half of the kite's material, so her section will be a triangle 4 feet high. It will still be 16 feet across when she splits it. So her part of the kite will look like this:

obtuse triangle with base 16 feet and height 4 feet

We have an obtuse triangle with a base of 16 feet and a height of 4 feet. We can plug those values into our area equation:

A = 1/2 (16 * 4)
A = 1/2 * 64
A = 32

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