Obtuse Triangle Practice Problems & Exercises Online

Master obtuse triangles with interactive practice problems. Learn to identify obtuse angles, calculate missing angles, and solve triangle classification exercises step-by-step.

📚What You'll Master in Obtuse Triangle Practice
  • Identify obtuse triangles by recognizing angles greater than 90 degrees
  • Calculate missing obtuse angles using the 180-degree triangle angle sum
  • Compare angle sizes in obtuse triangles to determine relationships
  • Solve algebraic equations to find unknown obtuse angle measurements
  • Classify triangles as obtuse, acute, or right using the Pythagorean theorem
  • Apply obtuse triangle properties to solve real-world geometry problems

Understanding Obtuse Triangle

Complete explanation with examples

Obtuse Triangle Definition

An obtuse triangle is a triangle that has one obtuse angle (greater than 90° 90° degrees and less than 180° 180° degrees) and two acute angles (each of which is less than 90° 90° degrees). The sum of all three angles together is 180° 180° degrees.

Detailed explanation

Practice Obtuse Triangle

Test your knowledge with 20 quizzes

Given the values of the sides of a triangle, is it a triangle with different sides?

282828252525AAABBBCCC28

Examples with solutions for Obtuse Triangle

Step-by-step solutions included
Exercise #1

Is the triangle in the drawing an acute-angled triangle?

Step-by-Step Solution

An acute-angled triangle is defined as a triangle where all three interior angles are less than 9090^\circ.

In examining the visual depiction of the triangle provided in the problem, we need to see if it appears to satisfy this property. The assessment relies on observing the triangle's structure shown in the drawing and noting any geometric indications suggesting angle types.

Given the information from the drawing, if all angles seem to satisfy the condition of being less than 9090^\circ, then by definition, the triangle is an acute-angled triangle.

Conclusively, the answer to whether the triangle is acute-angled based on provided visual assessment and inherent assumptions in its illustration is: Yes.

Answer:

Yes

Video Solution
Exercise #2

In an isosceles triangle, the angle between ? and ? is the "base angle".

Step-by-Step Solution

An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."

Therefore, the correct choice is Side, base.

Answer:

Side, base.

Exercise #3

Given the values of the sides of a triangle, is it a triangle with different sides?

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Step-by-Step Solution

As is known, a scalene triangle is a triangle in which each side has a different length.

According to the given information, this is indeed a triangle where each side has a different length.

Answer:

Yes

Video Solution
Exercise #4

Is the triangle in the drawing a right triangle?

Step-by-Step Solution

Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.

Answer:

Yes

Exercise #5

In an isosceles triangle, what are each of the two equal sides called ?

Step-by-Step Solution

In an isosceles triangle, there are three sides: two sides of equal length and one distinct side. Our task is to identify what the equal sides are called.

To address this, let's review the basic properties of an isosceles triangle:

  • An isosceles triangle is defined as a triangle with at least two sides of equal length.
  • The side that is different in length from the other two is usually called the "base" of the triangle.
  • The two equal sides of an isosceles triangle are referred to as the "legs."

Therefore, each of the two equal sides in an isosceles triangle is called a "leg."

In our problem, we confirm that the correct terminology for these two equal sides is indeed "legs," distinguishing them from the "base," which is the unequal side. This aligns with both the typical definitions and properties of an isosceles triangle.

Thus, the equal sides in an isosceles triangle are known as legs.

Answer:

Legs

Frequently Asked Questions

What makes a triangle obtuse?

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An obtuse triangle has one angle greater than 90° but less than 180°, and two acute angles less than 90°. The sum of all three angles always equals 180°, just like any triangle.

How do you find the obtuse angle in a triangle?

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To find an obtuse angle: 1) Add the two known acute angles, 2) Subtract their sum from 180°, 3) The result is your obtuse angle. Remember, the obtuse angle is always the largest angle in the triangle.

Can a triangle have two obtuse angles?

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No, a triangle cannot have two obtuse angles. Since each obtuse angle is greater than 90°, two obtuse angles would sum to more than 180°, which exceeds the total angle sum possible in any triangle.

What's the difference between obtuse and acute triangles?

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Obtuse triangles have one angle greater than 90°, while acute triangles have all three angles less than 90°. Obtuse triangles appear "wider" or more "spread out" compared to the sharper appearance of acute triangles.

How do you use the Pythagorean theorem to identify obtuse triangles?

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For sides a, b, and c (where c is longest): If a² + b² < c², the triangle is obtuse. If a² + b² = c², it's right. If a² + b² > c², it's acute.

What are common mistakes when solving obtuse triangle problems?

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Common errors include: forgetting that only ONE angle can be obtuse, miscalculating the 180° angle sum, confusing obtuse angles (>90°) with reflex angles (>180°), and incorrectly applying the Pythagorean theorem for classification.

Are obtuse triangles used in real life?

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Yes! Obtuse triangles appear in architecture (roof designs), engineering (bridge supports), art (geometric patterns), and navigation (triangulation methods). Understanding their properties helps in construction and design fields.

What formulas do I need for obtuse triangle practice problems?

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Key formulas include: Angle sum (A + B + C = 180°), Pythagorean test (a² + b² vs c²), and basic algebraic manipulation for solving angle relationships like A = 2B or C = ½A.

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