Solve Similar Triangles Calculator
Find unknown sides and angles in similar triangles using proportional relationships and scale factors
Similar Triangles Solver
Triangle 1 (Reference Triangle)
Side Correspondence
Triangle 2 (Similar Triangle)
Enter at least one known side to determine the scale factor
Results
Triangle 1 (Complete)
Triangle 2 (Similar)
Step-by-step Solution
Real-world Applications
Shadow Height Problem
Problem: A person 6 feet tall casts a 4-foot shadow. At the same time, a tree casts a 20-foot shadow. How tall is the tree?
Solution: Using similar triangles:
Person's height / Person's shadow = Tree's height / Tree's shadow
6 / 4 = Tree height / 20
Tree height = 30 feet
Scale Model Problem
Problem: A scale model of a building is 1:100. If the model is 25 cm tall, how tall is the actual building?
Solution: Using scale factor:
Scale factor = 100 (actual to model)
Actual height = 25 cm × 100 = 2500 cm
Building height = 25 meters
Similar Triangles Properties
Corresponding Angles
Corresponding Sides
Scale Factor
Similarity Criteria
AAA (Angle-Angle-Angle)
All corresponding angles are equal
SSS (Side-Side-Side)
All corresponding sides are proportional
SAS (Side-Angle-Side)
Two sides proportional, included angle equal
Key Formulas
Understanding Similar Triangles
What are Similar Triangles?
Similar triangles are triangles that have the same shape but different sizes. They have equal corresponding angles and proportional corresponding sides. The ratio between corresponding sides is called the scale factor.
Scale Factor
Scale Factor = Length₂ ÷ Length₁
The scale factor tells us how many times larger or smaller the similar triangle is compared to the original triangle.
Solving Similar Triangles
To solve similar triangles, follow these steps:
- Identify corresponding sides and angles
- Calculate the scale factor using known corresponding sides
- Apply the scale factor to find unknown sides
- Verify that angles remain equal in both triangles
Proportional Relationship:
a/A = b/B = c/C = k
where k is the scale factor
Real-world Applications
Architecture
Scale models and blueprints use similar triangles for proportional design
Navigation
Triangulation and distance measurement using similar triangle principles
Photography
Perspective and scaling in photography and computer graphics