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If the angles of the triangle are in the ratio of 1 : 4 : 7, the find the ratio of the greatest angle to the smallest angle?
- a)7 : 2
- b)2 : 3
- c)7 : 1
- d)3 : 5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the angles of the triangle are in the ratio of 1 : 4 : 7, the find ...
Let the angles of a triangles are in the ratio of x : 4x : 7x
We know that sum of the angles in a triangle = 180°
⇒ x + 4x + 7x = 180°
⇒ 12x = 180
⇒ x = 15°
∴ Smallest angle = 15°
Greatest angle = 7x = 7(15) = 105°
Ratio of the greatest angle to the smallest angle = 105 : 15 = 7 : 1
Most Upvoted Answer
If the angles of the triangle are in the ratio of 1 : 4 : 7, the find ...
Understanding the Triangle's Angle Ratio
To solve the problem, we start by understanding the relationship between the angles of the triangle given by the ratio 1 : 4 : 7.
Step 1: Define the Angles
- Let the angles be represented as:
- Smallest angle = x
- Second angle = 4x
- Greatest angle = 7x
Step 2: Sum of Angles in a Triangle
- The sum of the angles in any triangle is always 180 degrees.
- Therefore, we can set up the equation:
- x + 4x + 7x = 180
Step 3: Solve for x
- Combining like terms, we get:
- 12x = 180
- Now, divide both sides by 12:
- x = 15
Step 4: Calculate the Angles
- Now substituting x back into our angle definitions:
- Smallest angle = 15 degrees
- Second angle = 4 * 15 = 60 degrees
- Greatest angle = 7 * 15 = 105 degrees
Step 5: Find the Ratio of Greatest to Smallest Angle
- Now, we need to find the ratio of the greatest angle (105 degrees) to the smallest angle (15 degrees):
- Ratio = 105 : 15
- Simplifying this ratio:
- 105 ÷ 15 = 7
- 15 ÷ 15 = 1
- Therefore, the ratio is 7 : 1.
Conclusion
- The ratio of the greatest angle to the smallest angle is indeed 7 : 1, confirming that the correct answer is option 'C'.
To solve the problem, we start by understanding the relationship between the angles of the triangle given by the ratio 1 : 4 : 7.
Step 1: Define the Angles
- Let the angles be represented as:
- Smallest angle = x
- Second angle = 4x
- Greatest angle = 7x
Step 2: Sum of Angles in a Triangle
- The sum of the angles in any triangle is always 180 degrees.
- Therefore, we can set up the equation:
- x + 4x + 7x = 180
Step 3: Solve for x
- Combining like terms, we get:
- 12x = 180
- Now, divide both sides by 12:
- x = 15
Step 4: Calculate the Angles
- Now substituting x back into our angle definitions:
- Smallest angle = 15 degrees
- Second angle = 4 * 15 = 60 degrees
- Greatest angle = 7 * 15 = 105 degrees
Step 5: Find the Ratio of Greatest to Smallest Angle
- Now, we need to find the ratio of the greatest angle (105 degrees) to the smallest angle (15 degrees):
- Ratio = 105 : 15
- Simplifying this ratio:
- 105 ÷ 15 = 7
- 15 ÷ 15 = 1
- Therefore, the ratio is 7 : 1.
Conclusion
- The ratio of the greatest angle to the smallest angle is indeed 7 : 1, confirming that the correct answer is option 'C'.
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If the angles of the triangle are in the ratio of 1 : 4 : 7, the find the ratio of the greatest angle to the smallest angle?a)7 : 2b)2 : 3c)7 : 1d)3 : 5Correct answer is option 'C'. Can you explain this answer?
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