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 an acute-angled triangle?

Examples with solutions for Acute triangle

Step-by-step solutions included
Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer:

Right triangle

Video Solution
Exercise #2

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 #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer:

Obtuse Triangle

Video Solution
Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer:

Isosceles triangle

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?

+
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?

+
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°?

+
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?

+
• 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?

+
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?

+
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?

+
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?

+
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.

More Acute triangle Questions

Continue Your Math Journey

Practice by Question Type