Triangle Classification: Identifying an Obtuse Angle in Given Diagram

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

Compare the angle to a right angle (90°) - imagine a square corner. If the angle opens wider than a square corner, it's obtuse. If it's narrower, it's acute.

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 180°.

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

Acute triangle: All three angles less than 90°Right triangle: One angle exactly 90°Obtuse triangle: One angle greater than 90°

Q: Does the longest side always create the obtuse angle?

Yes! In any triangle, the largest angle is always opposite the longest side. So if you see a very long side, check the angle across from it - that's where the obtuse angle will be.

Q: How do I check my answer when identifying triangle types?

Use the visual test: Hold up your finger to form a right angle (90°) and compare it to each angle in the triangle. The obtuse angle should look noticeably wider than your finger corner.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's decide if this triangle is an obtuse triangle.

00:09 First, draw a line perpendicular to one side of the triangle.

00:13 Next, find the right angle and compare it with our angle.

00:18 If our angle is bigger than ninety degrees, it is obtuse.

00:23 Great job! This means our triangle is an obtuse triangle.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Does the diagram show an obtuse triangle?

2

Step-by-step solution

To determine if the triangle shown in the diagram is obtuse, we proceed as follows:

Step 1: Identify that the diagram is indeed a triangle by observing the confluence of three edges forming a closed shape.
Step 2: Appreciate the geometric arrangement of the triangle, focusing on the sides' lengths and angles visually.
Step 3: Noticeably, the longest side of the triangle represents a noticeable tilt indicating the presence of an obtuse angle.

Based on the observation above, notably from the triangle's longest side against the base, it's clear that one angle is larger than $90^\circ$ . Hence, the triangle in the diagram is indeed an obtuse triangle.

Therefore, the correct answer is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Obtuse triangle has one angle greater than 90 degrees
Visual Check: Look for wide angles that appear larger than right angles
Verification: Compare suspected obtuse angle to a square corner reference ✓

Common Mistakes

Avoid these frequent errors

Assuming all triangles with long sides are obtuse
Don't automatically think long sides = obtuse triangle! Side length alone doesn't determine angle size. A triangle can have very different side lengths but still have all acute angles. Always focus on the actual angle openings, not just side proportions.

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?

+

Compare the angle to a right angle (90°) - imagine a square corner. If the angle opens wider than a square corner, it's obtuse. If it's narrower, it's acute.

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 180°.

What's the difference between obtuse, acute, and right triangles?

+

Acute triangle: All three angles less than 90°
Right triangle: One angle exactly 90°
Obtuse triangle: One angle greater than 90°

Does the longest side always create the obtuse angle?

+

Yes! In any triangle, the largest angle is always opposite the longest side. So if you see a very long side, check the angle across from it - that's where the obtuse angle will be.

How do I check my answer when identifying triangle types?

+

Use the visual test: Hold up your finger to form a right angle (90°) and compare it to each angle in the triangle. The obtuse angle should look noticeably wider than your finger corner.

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Triangle Classification: Identifying an Obtuse Angle in Given Diagram

Triangle Classification with Visual Angle Analysis

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