Right Triangle Practice Problems & Exercises Online

Master right triangle concepts with interactive practice problems. Learn to identify 90-degree angles, calculate missing angles, and solve real-world applications.

📚What You'll Master in Right Triangle Practice
  • Identify right triangles by recognizing the 90-degree angle property
  • Calculate missing acute angles using the 180-degree triangle sum rule
  • Apply complementary angle relationships in right triangle problems
  • Solve step-by-step exercises involving angle measurements and calculations
  • Master real-world applications of right triangle angle properties
  • Build confidence through guided practice with immediate feedback

Understanding Types of Triangles

Complete explanation with examples

Definition of a right triangle

A right triangle is a triangle that has one right angle, meaning an angle of 90 degrees. Based on the fact that the sum of angles in any triangle is 180 degrees, we can conclude that the sum of the two remaining angles in a right triangle is 90 degrees. This means that both angles must be acute (less than 90 degrees).

Right Triangle

Detailed explanation

Practice Types of Triangles

Test your knowledge with 20 quizzes

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

Examples with solutions for Types of Triangles

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 a right triangle?

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A right triangle is defined by having exactly one right angle (90 degrees). Since all triangle angles sum to 180 degrees, the other two angles must be acute and add up to 90 degrees.

How do I find missing angles in a right triangle?

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Use the fact that angles in a triangle sum to 180°. If one angle is 90° and you know another angle, subtract both from 180° to find the third angle. For example: 180° - 90° - 45° = 45°.

Are both non-right angles in a right triangle always acute?

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Yes, both remaining angles must be acute (less than 90°). Since they must sum to 90° (because 180° - 90° = 90°), neither can be 90° or greater.

What are complementary angles in right triangles?

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In a right triangle, the two acute angles are complementary, meaning they add up to 90°. If one acute angle is 30°, the other must be 60° (30° + 60° = 90°).

Can a right triangle have two 45-degree angles?

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Yes! This creates a 45-45-90 triangle, which is a special right triangle. The angles are 45°, 45°, and 90°, and they sum to 180° as required.

How do I solve right triangle angle problems step by step?

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Follow these steps: 1) Identify the right angle (90°), 2) Write down any given angles, 3) Use the equation: missing angle = 180° - 90° - known acute angle, 4) Check that all three angles sum to 180°.

What are common mistakes when working with right triangles?

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Common errors include: forgetting that one angle must be exactly 90°, not using the triangle sum theorem correctly, and confusing complementary angles (sum to 90°) with supplementary angles (sum to 180°).

Why do right triangle problems matter in real life?

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Right triangles appear in construction, navigation, engineering, and design. Understanding angle relationships helps solve problems involving ramps, roofs, ladders, and any situation involving perpendicular measurements.

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