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If a triangle has angles measuring 30°, 60°, and 90°, which side is the longest?
- a)The side opposite the 30° angle
- b)The side opposite the 60° angle
- c)The side opposite the 90° angle
- d)All sides are equal
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If a triangle has angles measuring 30°, 60°, and 90°, which side is th...
In a right triangle, the side opposite the right angle (90°) is the longest side, called the hypotenuse.
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Most Upvoted Answer
If a triangle has angles measuring 30°, 60°, and 90°, which side is th...
Understanding Triangle Angles
In a triangle, the relationship between the angles and the lengths of the sides is crucial. The side opposite the largest angle is always the longest.
Characteristics of a 30°-60°-90° Triangle
- A triangle with angles measuring 30°, 60°, and 90° is a special right triangle.
- In this triangle, the angles are distinct, where:
- 30° is the smallest angle
- 60° is the medium angle
- 90° is the largest angle
Identifying the Longest Side
- The side opposite the 90° angle is the longest side.
- This side is known as the hypotenuse.
Side Length Relationships
- In a 30°-60°-90° triangle, the ratio of the lengths of the sides is:
- The side opposite the 30° angle is the shortest.
- The side opposite the 60° angle is longer than the side opposite the 30° but shorter than the hypotenuse.
- The side opposite the 90° angle (the hypotenuse) is the longest.
Conclusion
Therefore, the correct answer is:
- Option C: The side opposite the 90° angle is the longest side.
This understanding of triangle properties and side relationships is essential for solving various geometric problems.
In a triangle, the relationship between the angles and the lengths of the sides is crucial. The side opposite the largest angle is always the longest.
Characteristics of a 30°-60°-90° Triangle
- A triangle with angles measuring 30°, 60°, and 90° is a special right triangle.
- In this triangle, the angles are distinct, where:
- 30° is the smallest angle
- 60° is the medium angle
- 90° is the largest angle
Identifying the Longest Side
- The side opposite the 90° angle is the longest side.
- This side is known as the hypotenuse.
Side Length Relationships
- In a 30°-60°-90° triangle, the ratio of the lengths of the sides is:
- The side opposite the 30° angle is the shortest.
- The side opposite the 60° angle is longer than the side opposite the 30° but shorter than the hypotenuse.
- The side opposite the 90° angle (the hypotenuse) is the longest.
Conclusion
Therefore, the correct answer is:
- Option C: The side opposite the 90° angle is the longest side.
This understanding of triangle properties and side relationships is essential for solving various geometric problems.
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Solutions for If a triangle has angles measuring 30°, 60°, and 90°, which side is the longest?a)The side opposite the 30° angleb)The side opposite the 60° anglec)The side opposite the 90° angled)All sides are equalCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 5.
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