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In a right triangle, if one angle is 30 degrees, what is the measure of the angl

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Question: In a right triangle, if one angle is 30 degrees, what is the measure of the angle opposite the side that is half the length of the hypotenuse?

Options:

  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 45 degrees

Correct Answer: 30 degrees

Solution: 

In a 30-60-90 triangle, the side opposite the 30-degree angle is half the hypotenuse.

In a right triangle, if one angle is 30 degrees, what is the measure of the angl

Practice Questions

Q1
In a right triangle, if one angle is 30 degrees, what is the measure of the angle opposite the side that is half the length of the hypotenuse?
  1. 30 degrees
  2. 60 degrees
  3. 90 degrees
  4. 45 degrees

Questions & Step-by-Step Solutions

In a right triangle, if one angle is 30 degrees, what is the measure of the angle opposite the side that is half the length of the hypotenuse?
  • Step 1: Identify that we have a right triangle with one angle measuring 30 degrees.
  • Step 2: Recall that in a right triangle, the angles add up to 180 degrees.
  • Step 3: Since one angle is 90 degrees (the right angle) and another is 30 degrees, calculate the third angle: 180 - 90 - 30 = 60 degrees.
  • Step 4: Recognize that in a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse.
  • Step 5: Conclude that the angle opposite the side that is half the length of the hypotenuse is 30 degrees.
  • 30-60-90 Triangle Properties – In a 30-60-90 triangle, the side lengths 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 the hypotenuse multiplied by √3/2.
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