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High School Geometry: Homework Help Resource13 chapters | 142 lessons

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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.

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.

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.

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

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

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.

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

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.

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.

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:

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

Mary will need to buy 32 square feet of material for her part of the kite.

Meanwhile, Janet, not to be outdone, wants to make a kite by herself that's 30 feet across and 10 feet wide. How much material will she need for the whole kite?

Her kite will look like this:

What we really have are two obtuse triangles with a 30-foot common base. The height of each triangle will be half of the kite's 10-foot width. 10 / 2 = 5. So the height of each triangle is 5 feet.

We can plug the base length of 30 and the height of 5 into our area equation to get the area of one of the two triangles:

*A* = 1/2 (30 * 5)*A* = 1/2 * 150*A* = 75

The area of one triangle is 75 square feet. To get the area of the entire kite, we just need to double that since there are two obtuse triangles in the kite.

75 * 2 = 150

Janet will need to buy 150 square feet of material to make her kite.

An **obtuse angle** is any angle larger than 90 degrees. An **obtuse triangle** is a triangle containing an obtuse angle. The formula for an obtuse triangle's **area** is:

*A = 1/2 (b * h)*

Where *b* is the length of the triangle's base and *h* is the triangle's height. Any side of the triangle can be selected as the base. To find the height, we extend a perpendicular line from the base to the opposite vertex.

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High School Geometry: Homework Help Resource13 chapters | 142 lessons

- Area of Triangles and Rectangles 5:43
- Perimeter of Triangles and Rectangles 8:54
- How to Identify Similar Triangles 7:23
- Angles and Triangles: Practice Problems 7:43
- Triangles: Definition and Properties 4:30
- Classifying Triangles by Angles and Sides 5:44
- Interior and Exterior Angles of Triangles: Definition & Examples 5:25
- Constructing the Median of a Triangle 4:47
- Median, Altitude, and Angle Bisectors of a Triangle 4:50
- Constructing Triangles: Types of Geometric Construction 5:59
- Properties of Concurrent Lines in a Triangle 6:17
- Perfect Numbers: Definition, Formula & Examples 6:15
- Pyramid in Math: Definition & Practice Problems 5:31
- Supplementary Angle: Definition & Theorem 4:29
- Transversal in Geometry: Definition & Angles 3:06
- What is a Hexagon? - Definition, Area & Angles 3:28
- What is a Right Angle? - Definition & Formula 3:19
- What is a Straight Angle? - Definition & Example 3:08
- What is an Obtuse Angle? - Definition & Examples 2:35
- What Is an Obtuse Triangle? - Definition & Area Formula 4:38
- Go to Properties of Triangles: Homework Help

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