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SAT Practice Questions: 30-60-90 Triangles

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Updated:  
2017-01-28 1:13:14
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From The Book:  
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When you encounter a question on the SAT Math exam where you have to find the area of a triangle, you may end up treating it as a 30-60-90 triangle, even if it's equilateral. (Fun fact: an equilateral triangle can be thought of as two 30-60-90 triangles!)

The following practice questions ask you to find the area of an equilateral triangle and then to find the area of a right triangle given only its hypotenuse and one of its angles.

Practice questions

  1. What is the area of an equilateral triangle with a base of 4? SAT1001_eq0801
  2. A certain right triangle has a hypotenuse of 2. If one of the angles is 30 degrees, what is the area of the triangle? SAT1001_eq0802

Answers and explanations

  1. The correct answer is Choice (A). You can find the area of an equilateral triangle by using the formula SAT1001_eq0803 where s is any of the sides, including the base: SAT1001_eq0804 You can also consider the equilateral triangle to be two 30-60-90 triangles, giving the triangle a height of SAT1001_eq0805 then use the SAT1001_eq0806
  2. The correct answer is Choice (A). If one of the angles is 30 degrees, the other angle is 60 degrees, making this a 30-60-90 triangle, with a side ratio of SAT1001_eq0807 The 2 is the hypotenuse, making the other two sides 1 and SAT1001_eq0808 These numbers are also the base and height, so plug them into the formula for the area of a triangle: SAT1001_eq0809

About This Article

This article is from the book: 

About the book author:

Ron Woldoff, MBA, is the founder of National Test Prep, where he helps students achieve their goals on the SAT, GMAT®, and GRE®. He teaches prep courses at Arizona and is the author of several test-prep books.