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In a right triangle, if one angle is 30 degrees, what is the ratio of the length

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Question: In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees?

Options:

  1. 1:√3
  2. 1:2
  3. √3:1
  4. 2:1

Correct Answer: 1:√3

Solution: 

In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees are in the ratio 1:√3.

In a right triangle, if one angle is 30 degrees, what is the ratio of the length

Practice Questions

Q1
In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees?
  1. 1:√3
  2. 1:2
  3. √3:1
  4. 2:1

Questions & Step-by-Step Solutions

In a right triangle, if one angle is 30 degrees, what is the ratio of the lengths of the sides opposite to the 30 degrees and 60 degrees?
  • Step 1: Understand that a right triangle has one angle that is 90 degrees.
  • Step 2: Recognize that if one angle is 30 degrees, the other non-right angle must be 60 degrees (since 30 + 60 + 90 = 180).
  • Step 3: Identify that this triangle is a special type called a 30-60-90 triangle.
  • Step 4: Learn the properties of a 30-60-90 triangle: the side opposite the 30-degree angle is the shortest and is often labeled as '1'.
  • Step 5: The side opposite the 60-degree angle is longer and is equal to '√3' times the length of the side opposite the 30-degree angle.
  • Step 6: Therefore, the ratio of the lengths of the sides opposite the 30 degrees and 60 degrees is 1:√3.
  • 30-60-90 Triangle Ratios – In a 30-60-90 triangle, the lengths of the sides are in a specific ratio: the side opposite the 30-degree angle is half the hypotenuse, and the side opposite the 60-degree angle is √3/2 times the hypotenuse.
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