Acute Triangle Practice Problems - Types of Triangles

Master acute triangles with step-by-step practice problems. Learn to identify and classify triangles by angles using the Pythagorean theorem and angle measurements.

📚What You'll Master in These Acute Triangle Practice Problems
  • Identify acute triangles by checking if all angles are less than 90°
  • Use the Pythagorean theorem to classify triangles as acute, obtuse, or right
  • Apply angle sum properties to determine if three angles can form a triangle
  • Compare side lengths to determine triangle type using mathematical inequalities
  • Solve real-world problems involving acute triangle identification and classification
  • Distinguish between acute, obtuse, and right triangles using multiple methods

Understanding Acute triangle

Complete explanation with examples

Definition of Acute Triangle

An acute triangle has all acute angles, meaning each of its three angles measures less than 90° 90° degrees and the sum of all three together equals 180° 180° degrees. 

Detailed explanation

Practice Acute triangle

Test your knowledge with 20 quizzes

Is the triangle in the drawing a right triangle?

Examples with solutions for Acute 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

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer:

Isosceles triangle

Video Solution
Exercise #4

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

9.19.19.19.59.59.5AAABBBCCC9

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 #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer:

Equilateral triangle

Video Solution

Frequently Asked Questions

What makes a triangle an acute triangle?

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An acute triangle has all three angles measuring less than 90 degrees. The sum of all angles still equals 180°, but each individual angle is acute (less than 90°).

How do you identify an acute triangle using side lengths?

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Use the Pythagorean theorem: if a² + b² > c² (where c is the longest side), then the triangle is acute. If the sum of squares of the two shorter sides is greater than the square of the longest side, all angles are acute.

Can a triangle have angles of 70°, 60°, and 50°?

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Yes, this forms an acute triangle. All three angles are less than 90°, and they sum to 180° (70° + 60° + 50° = 180°), satisfying both requirements for a valid acute triangle.

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

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• Acute triangle: All angles < 90° • Right triangle: One angle = 90° • Obtuse triangle: One angle > 90° The angle sum is always 180° for all triangles.

How do you solve triangle classification problems step by step?

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1. Identify the longest side (potential hypotenuse) 2. Apply the Pythagorean theorem: compare a² + b² to c² 3. If a² + b² > c², it's acute; if equal, it's right; if less, it's obtuse

Why can't angles of 90°, 115°, and 35° form a triangle?

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These angles sum to 240°, which exceeds the required 180° for any triangle. The fundamental rule is that interior angles of any triangle must always sum to exactly 180°.

What are common mistakes when identifying acute triangles?

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Students often forget to check ALL angles are less than 90°, or incorrectly apply the Pythagorean theorem by not identifying the longest side first. Always verify the angle sum equals 180°.

Can an equilateral triangle be an acute triangle?

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Yes, an equilateral triangle is always acute because each angle measures exactly 60°, which is less than 90°. It's the most common example of an acute triangle.

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