Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S3-SA2-0038
What is an Obtuse-Angled Triangle?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
An obtuse-angled triangle is a triangle where one of its three interior angles is greater than 90 degrees but less than 180 degrees. Remember, a triangle always has three sides and three angles, and the sum of all its angles is always 180 degrees.
Simple Example
Quick Example
Imagine you are looking at a slice of pizza. If the angle at the tip of the slice (where all the crusts meet) is wider than a perfectly square corner (90 degrees), but not completely flat (180 degrees), then that pizza slice forms an obtuse angle. If a triangle has one such angle, it's an obtuse-angled triangle.
Worked Example
Step-by-Step
Let's check if a triangle with angles 30 degrees, 40 degrees, and 110 degrees is an obtuse-angled triangle.
Step 1: Identify all the angles given in the triangle. The angles are 30 degrees, 40 degrees, and 110 degrees.
---Step 2: Check if any of these angles are greater than 90 degrees. We see that 110 degrees is greater than 90 degrees.
---Step 3: Check if this angle is less than 180 degrees. 110 degrees is indeed less than 180 degrees.
---Step 4: Since one angle (110 degrees) is between 90 degrees and 180 degrees, it is an obtuse angle.
---Step 5: Since the triangle has one obtuse angle, it is an obtuse-angled triangle.
Answer: Yes, it is an obtuse-angled triangle.
Why It Matters
Understanding different types of triangles is crucial in many fields. Engineers use this knowledge when designing buildings or bridges to ensure stability, and game developers use it to create realistic shapes and movements in virtual worlds. Even in data science, understanding geometric shapes helps visualize and analyze complex data patterns.
Common Mistakes
MISTAKE: Thinking an obtuse angle can be exactly 90 degrees or 180 degrees. | CORRECTION: An obtuse angle must be strictly greater than 90 degrees and strictly less than 180 degrees. An angle of 90 degrees is a right angle, and 180 degrees is a straight angle.
MISTAKE: Believing a triangle can have more than one obtuse angle. | CORRECTION: A triangle can only have one obtuse angle. If it had two, the sum of its angles would already exceed 180 degrees, which is impossible for a triangle.
MISTAKE: Confusing an obtuse-angled triangle with an obtuse angle itself. | CORRECTION: An obtuse angle is just one angle measurement. An obtuse-angled triangle is a complete triangle shape that contains one such obtuse angle.
Practice Questions
Try It Yourself
QUESTION: A triangle has angles 25 degrees, 35 degrees, and 120 degrees. Is it an obtuse-angled triangle? | ANSWER: Yes
QUESTION: Can a triangle have angles 100 degrees, 50 degrees, and 40 degrees? If yes, what type of triangle is it? | ANSWER: No, the sum of angles is 190 degrees, which is not possible for a triangle.
QUESTION: If two angles of a triangle are 20 degrees and 70 degrees, what is the measure of the third angle? Is this an obtuse-angled triangle? | ANSWER: The third angle is 180 - (20 + 70) = 180 - 90 = 90 degrees. No, it is a right-angled triangle.
MCQ
Quick Quiz
Which of the following sets of angles can form an obtuse-angled triangle?
60, 60, 60
90, 45, 45
110, 30, 40
80, 70, 30
The Correct Answer Is:
C
Option C (110, 30, 40) forms a valid triangle because the angles sum to 180 degrees, and one angle (110 degrees) is greater than 90 degrees, making it obtuse. The other options either have no obtuse angle or form a right-angled triangle.
Real World Connection
In the Real World
You might see obtuse angles in the design of a roof for a house, especially in hilly areas where sloped roofs are common. Architects use these angles to ensure water runoff and structural stability. Even the blades of a ceiling fan, when viewed from certain angles, can form obtuse angles, which are important for air circulation.
Key Vocabulary
Key Terms
TRIANGLE: A polygon with three sides and three angles | ANGLE: The space between two intersecting lines or surfaces | OBTUSE ANGLE: An angle greater than 90 degrees but less than 180 degrees | DEGREES: A unit of measurement for angles
What's Next
What to Learn Next
Great job learning about obtuse-angled triangles! Next, you should explore 'Acute-Angled Triangles' and 'Right-Angled Triangles'. Understanding all three types will give you a complete picture of how triangles are classified based on their angles.
