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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 90 degrees angles?

Options:

  1. 1:2
  2. 1:√3
  3. 1:1
  4. 2:1

Correct Answer: 1:2

Solution: 

In a 30-60-90 triangle, the ratio of the sides opposite the 30° and 90° angles is 1:2.

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 90 degrees angles?
  1. 1:2
  2. 1:√3
  3. 1:1
  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 90 degrees angles?
  • Step 1: Understand that in a right triangle, one angle is 90 degrees.
  • Step 2: Recognize that if one angle is 30 degrees, the other angle must be 60 degrees (since 30 + 60 + 90 = 180).
  • Step 3: Identify the sides of the triangle: the side opposite the 30-degree angle is the shortest side.
  • Step 4: In a special type of triangle called a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse (the side opposite the 90-degree angle).
  • Step 5: Therefore, the ratio of the length of the side opposite the 30-degree angle to the length of the side opposite the 90-degree angle (the hypotenuse) is 1:2.
  • 30-60-90 Triangle Ratios – In a 30-60-90 triangle, the sides are in the ratio of 1 (opposite 30°) : √3 (opposite 60°) : 2 (opposite 90°).
  • Right Triangle Properties – Understanding the properties of right triangles, particularly the relationships between angles and side lengths.
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