Obtuse Triangle Analysis: Visual Angle Measurement Challenge

Q: How can I tell if an angle is obtuse just by looking?

Look for angles that open wider than a square corner. If you imagine placing a book corner (90°) at the vertex, an obtuse angle will extend beyond both edges of the corner.

Q: Can a triangle have more than one obtuse angle?

No! A triangle can have at most one obtuse angle. Since all angles must add up to $180°$, having two obtuse angles (each > 90°) would exceed this limit.

Q: What's the difference between obtuse and acute triangles?

Obtuse triangles have one angle > 90°, while acute triangles have all angles Right triangles have exactly one 90° angle.

Q: Do I need to measure exact degrees?

For visual problems like this, estimation is usually sufficient. Just compare angles to familiar 90° references like book corners, door frames, or square tiles.

Q: Why does the diagram matter for classification?

The visual representation helps you identify angle sizes without calculations. Look at how the sides meet - wide openings suggest obtuse angles, while narrow ones suggest acute angles.

Triangle Classification with Visual Angle Assessment

Does the diagram show an obtuse triangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is an obtuse triangle

00:03 Draw a perpendicular to the side

00:11 Identify the right angle and compare it to our angle

00:14 Our angle is greater than 90° (obtuse), therefore the triangle is obtuse

00:19 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Does the diagram show an obtuse triangle?

Step-by-step solution

To determine if the triangle in the diagram is obtuse, we will visually assess the angles:

Step 1: Identify the angles in the diagram. The triangle has three angles, with one angle appearing between the horizontal base and the left slanted side.
Step 2: Evaluate the angle between the base and the left side. If it opens wider than a right angle, it's considered obtuse. This angle seems to be greater than $90^\circ$ , indicating obtuseness.
Step 3: Conclude based on visual inspection. Since this key angle is greater than $90^\circ$ , the triangle must be an obtuse triangle.

Therefore, the solution to the problem is Yes; the diagram does show an obtuse triangle.

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Obtuse triangles have one angle greater than 90°
Technique: Compare angles visually to right angle squares or corners
Check: Verify that widest angle opens beyond perpendicular lines ✓

Common Mistakes

Avoid these frequent errors

Assuming triangles are acute without measuring angles
Don't just look at triangle shape and guess it's acute = wrong classification! Sharp-looking triangles can still have obtuse angles. Always examine each angle carefully and compare to 90° reference.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

How can I tell if an angle is obtuse just by looking?

Look for angles that open wider than a square corner. If you imagine placing a book corner (90°) at the vertex, an obtuse angle will extend beyond both edges of the corner.

Can a triangle have more than one obtuse angle?

No! A triangle can have at most one obtuse angle. Since all angles must add up to $180°$ , having two obtuse angles (each > 90°) would exceed this limit.

What's the difference between obtuse and acute triangles?

Obtuse triangles have one angle > 90°, while acute triangles have all angles < 90°. Right triangles have exactly one 90° angle.

Do I need to measure exact degrees?

For visual problems like this, estimation is usually sufficient. Just compare angles to familiar 90° references like book corners, door frames, or square tiles.

Why does the diagram matter for classification?

The visual representation helps you identify angle sizes without calculations. Look at how the sides meet - wide openings suggest obtuse angles, while narrow ones suggest acute angles.

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