Class 9 Exam > Class 9 Questions > In a ΔABC,∠A = 50°, ∠B = 60...
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In a ΔABC,∠A = 50°, ∠B = 60°. The longest side of the triangle will be
- a)AB
- b)BC
- c)CA
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a ΔABC,∠A = 50°, ∠B = 60°. The longest side o...
∠A = 50°, ∠B = 60°
∠C = 180° - (∠A + ∠B)
= 180° - 110°
= 70°
∵ ∠C is the largest angle of ΔABC
∴ AB is the largest side of ΔABC.
∠C = 180° - (∠A + ∠B)
= 180° - 110°
= 70°
∵ ∠C is the largest angle of ΔABC
∴ AB is the largest side of ΔABC.
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Community Answer
In a ΔABC,∠A = 50°, ∠B = 60°. The longest side o...
Understanding Triangle Properties
In triangle ABC, we are given the angles:
- Angle A = 50°
- Angle B = 60°
To determine the longest side, we need to utilize the property that states: the side opposite the largest angle is the longest side.
Calculating Angle C
First, we calculate the third angle (C) using the triangle angle sum property:
- Angle C = 180° - (Angle A + Angle B)
- Angle C = 180° - (50° + 60°) = 70°
Now we have all angles in triangle ABC:
- Angle A = 50°
- Angle B = 60°
- Angle C = 70°
Identifying the Longest Side
Next, we compare the angles to determine which is the largest:
- Angle A = 50°
- Angle B = 60°
- Angle C = 70° (Largest angle)
The side opposite the largest angle (Angle C) is side AB.
Conclusion
Since side AB is opposite the largest angle (70°), it is the longest side of triangle ABC.
Thus, the correct answer is:
- a) AB
This aligns with the triangle inequality property, confirming that side AB is indeed the longest side in triangle ABC.
In triangle ABC, we are given the angles:
- Angle A = 50°
- Angle B = 60°
To determine the longest side, we need to utilize the property that states: the side opposite the largest angle is the longest side.
Calculating Angle C
First, we calculate the third angle (C) using the triangle angle sum property:
- Angle C = 180° - (Angle A + Angle B)
- Angle C = 180° - (50° + 60°) = 70°
Now we have all angles in triangle ABC:
- Angle A = 50°
- Angle B = 60°
- Angle C = 70°
Identifying the Longest Side
Next, we compare the angles to determine which is the largest:
- Angle A = 50°
- Angle B = 60°
- Angle C = 70° (Largest angle)
The side opposite the largest angle (Angle C) is side AB.
Conclusion
Since side AB is opposite the largest angle (70°), it is the longest side of triangle ABC.
Thus, the correct answer is:
- a) AB
This aligns with the triangle inequality property, confirming that side AB is indeed the longest side in triangle ABC.
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