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A right triangle has one angle measuring 30 degrees. If the hypotenuse is 10, wh

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Question: A right triangle has one angle measuring 30 degrees. If the hypotenuse is 10, what is the length of the side opposite the 30-degree angle?

Options:

  1. 5
  2. 6
  3. 7
  4. 8

Correct Answer: 5

Solution: 

The side opposite the 30-degree angle is half the hypotenuse: 10 * 1/2 = 5.

A right triangle has one angle measuring 30 degrees. If the hypotenuse is 10, wh

Practice Questions

Q1
A right triangle has one angle measuring 30 degrees. If the hypotenuse is 10, what is the length of the side opposite the 30-degree angle?
  1. 5
  2. 6
  3. 7
  4. 8

Questions & Step-by-Step Solutions

A right triangle has one angle measuring 30 degrees. If the hypotenuse is 10, what is the length of the side opposite the 30-degree angle?
  • Step 1: Identify the triangle type. This is a right triangle with one angle measuring 30 degrees.
  • Step 2: Recall the properties of a 30-60-90 triangle. In this type of triangle, the side opposite the 30-degree angle is always half the length of the hypotenuse.
  • Step 3: Find the length of the hypotenuse. The hypotenuse is given as 10.
  • Step 4: Calculate the length of the side opposite the 30-degree angle by taking half of the hypotenuse: 10 * 1/2.
  • Step 5: Perform the calculation: 10 * 1/2 = 5.
  • Step 6: Conclude that the length of the side opposite the 30-degree angle is 5.
  • Properties of 30-60-90 Triangles – In a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse.
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