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If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled
Most Upvoted Answer
If the angles of a triangle are in the ratio 3 7 10 ,show that triangl...
Proof:
To prove that the triangle is right-angled, we need to show that one of the angles is equal to 90 degrees.
Let's assume the three angles of the triangle are 3x, 7x, and 10x, where x is a constant.
Ratio of Angles:
The sum of all angles in a triangle is 180 degrees. Therefore, we can write the equation as:
3x + 7x + 10x = 180
Simplifying the equation, we get:
20x = 180
Dividing both sides of the equation by 20, we find:
x = 9
Angles of the Triangle:
Now, we can substitute the value of x back into the equation to find the angles of the triangle:
Angle 1 = 3x = 3 * 9 = 27 degrees
Angle 2 = 7x = 7 * 9 = 63 degrees
Angle 3 = 10x = 10 * 9 = 90 degrees
Conclusion:
Therefore, the angles of the triangle are 27 degrees, 63 degrees, and 90 degrees. Since one angle is equal to 90 degrees, the triangle is right-angled.
Visually Appealing Presentation:
Proof:
1. Ratio of Angles:
- Sum of all angles in a triangle is 180 degrees.
- Equation: 3x + 7x + 10x = 180
- Simplifying: 20x = 180
- x = 9
2. Angles of the Triangle:
- Angle 1 = 3x = 3 * 9 = 27 degrees
- Angle 2 = 7x = 7 * 9 = 63 degrees
- Angle 3 = 10x = 10 * 9 = 90 degrees
Conclusion:
- The angles of the triangle are 27 degrees, 63 degrees, and 90 degrees.
- Since one angle is equal to 90 degrees, the triangle is right-angled.
To prove that the triangle is right-angled, we need to show that one of the angles is equal to 90 degrees.
Let's assume the three angles of the triangle are 3x, 7x, and 10x, where x is a constant.
Ratio of Angles:
The sum of all angles in a triangle is 180 degrees. Therefore, we can write the equation as:
3x + 7x + 10x = 180
Simplifying the equation, we get:
20x = 180
Dividing both sides of the equation by 20, we find:
x = 9
Angles of the Triangle:
Now, we can substitute the value of x back into the equation to find the angles of the triangle:
Angle 1 = 3x = 3 * 9 = 27 degrees
Angle 2 = 7x = 7 * 9 = 63 degrees
Angle 3 = 10x = 10 * 9 = 90 degrees
Conclusion:
Therefore, the angles of the triangle are 27 degrees, 63 degrees, and 90 degrees. Since one angle is equal to 90 degrees, the triangle is right-angled.
Visually Appealing Presentation:
Proof:
1. Ratio of Angles:
- Sum of all angles in a triangle is 180 degrees.
- Equation: 3x + 7x + 10x = 180
- Simplifying: 20x = 180
- x = 9
2. Angles of the Triangle:
- Angle 1 = 3x = 3 * 9 = 27 degrees
- Angle 2 = 7x = 7 * 9 = 63 degrees
- Angle 3 = 10x = 10 * 9 = 90 degrees
Conclusion:
- The angles of the triangle are 27 degrees, 63 degrees, and 90 degrees.
- Since one angle is equal to 90 degrees, the triangle is right-angled.
Community Answer
If the angles of a triangle are in the ratio 3 7 10 ,show that triangl...
U take the angles as x y z
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If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled.
If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angles of a triangle are in the ratio 3 7 10 ,show that triangle is right angled.
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