Lesson: Geometry - 21

30°/60°/90° Triangles

[Page 21 of 30]

A triangle where the angles are 30°, 60°, and 90°. If you draw an altitude in an equilateral triangle, you will form two congruent 30º- 60º- 90º triangles. Starting with the sides of the equilateral triangle to be 2, the Pythagorean Theorem will allow us to establish pattern relationships between the sides of a 30º- 60º- 90º triangle. These relationships will be stated here as "short cut formulas" that will allow us to quickly arrive at answers regarding side lengths without applying trigonometric functions, or other means.

Another triangle that you're almost sure to see on your standardized test is the 30°/60°/90° triangle. Often, you'll see it when an equilateral triangle is divided into two triangles of equal size. Learn the side-length ratio for the 30°/60°/90° triangle and you'll save yourself many calculations on test day.

If we set x as the length of the shortest side (the side opposite the 30° angle), then the side opposite the 60° angle has length x √3, and the hypotenuse has length 2x.

Hint

Back Next

Next to display next topic in the chapter.

Test Prep Lessons With Video Lessons and Explained MCQ

Large number of solved practice MCQ with explanations. Video Lessons and 10 Fully explained Grand/Full Tests.

Quantitative Aptitude Reasoning English General Knowledge Picture Patterns

Jobs in Pakistan Induction process Test Prep Sections Practice MCQs Admission Tests Test Sections Success on Tests Study in USA Pak Universities Employment ISSB Preliminaries Articles and Essays Schools & Colleges Study Abroad Career News

Arithmetic Geometry Data Interpretation Problem Solving Data Sufficiency Quant. Comparison

English Vocabulary English Correction Antonyms Synonyms Analogies Fill in the Blanks Critical Reading Text Completion

Number Series Picture Pattern Critical Reasoning Analytical Reasoning

Writing

Physics Chemistry Biology Mathematics Pak Penal Code Islamic Hudood Laws

Geometry Strategies Basic Lessons Intermediate Lessons Challenging Lessons Finding Degree Measurements Angles Vertical Angles Angles Terms And Rules Alternate Angles and Tranversal Triangles Triangles Lengths of Sides Triangles Side-Angle Relationship Popular Pythagorean Ratios Triangles Area Using Ratios Perimeter of Triangle 30-60-90 Triangles Rectangles Quadrilaterals Parallelograms Squares Areas Of Quadrilaterals Areas Of Rectangles And Squares Basics Next Steps Degree 45, degree 90,degree Isosceles Triangle

MCQ with question Explanations Scholarships and Financial Aid

Lesson: Geometry - 21

30°/60°/90° Triangles

Test Prep Lessons With Video Lessons and Explained MCQ

Current Menu

More for You

Problem Solving

Quantitative Comparison

PAF - Cadet Wing

You may be interested in

Colleges in Multan

Colleges in Peshawar

Study in Canada

Foreign Jobs in USA UK Australia and Canada

Join Pakistan Air Force

GRE Biology

Islamia College Peshawar

NUST - Medical and Bio Sciences

About us

Quick Test Prep

Study Abroad

Lesson: Geometry - 21

30°/60°/90° Triangles

Test Prep Lessons With Video Lessons and Explained MCQ

Current Menu

Main Menu (Click/Tap to Open)

Current Menu

Quantitative

Verbal

Logical/Reasoning

Writing

Subjects

Geometry

More for You

Problem Solving

Quantitative Comparison

PAF - Cadet Wing

You may be interested in

About us

Quick Test Prep

Study Abroad