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In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, wha

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Question: In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite to the 30-degree angle? (2019)

Options:

  1. 5 cm
  2. 10 cm
  3. 8 cm
  4. 7 cm

Correct Answer: 5 cm

Exam Year: 2019

Solution: 

The side opposite to the 30-degree angle is half the hypotenuse, so it is 10/2 = 5 cm.

In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, wha

Practice Questions

Q1
In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite to the 30-degree angle? (2019)
  1. 5 cm
  2. 10 cm
  3. 8 cm
  4. 7 cm

Questions & Step-by-Step Solutions

In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite to the 30-degree angle? (2019)
  • Step 1: Identify the right triangle and the given information: one angle is 30 degrees and the hypotenuse is 10 cm.
  • Step 2: Recall the property of a right triangle: in a 30-60-90 triangle, the side opposite the 30-degree angle is always half the length of the hypotenuse.
  • Step 3: Calculate the length of the side opposite the 30-degree angle by dividing the hypotenuse by 2: 10 cm / 2 = 5 cm.
  • Step 4: Conclude that the length of the side opposite the 30-degree angle is 5 cm.
  • Properties of Right Triangles – In a right triangle, the side opposite a 30-degree angle is always half the length of the hypotenuse.
  • Trigonometric Ratios – Understanding the relationship between angles and side lengths in right triangles using sine, cosine, and tangent.
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