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Directions: Kindly study the following Question carefully and choose the right answer:
The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.
- a)12
- b)10
- c)14
- d)16
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Directions: Kindly study the following Question carefully and choose t...
Given, AB = 12 cm, BC = 8 cm,
∠C = 59°
Let ∠A = Θ
∴ ∠B = 180° – (59° + Θ) = 121° – Θ
Now, let us see the choices. If AC = 12 cm, triangle would not be scalene. Hence, option A is ruled out. If AC =
10 cm, AB will become the largest side and ∠C the largest angle. But ∠C = 59°. Hence option B is ruled out. So,
AC is either 14 cm or 16 cm. In any case, ∠B will be the largest angle and ∠A (say Θ) the smallest:
Also, ∠B = 180° – (59° + Θ) = 121° – Θ
By sine formula
∠C = 59°
Let ∠A = Θ
∴ ∠B = 180° – (59° + Θ) = 121° – Θ
Now, let us see the choices. If AC = 12 cm, triangle would not be scalene. Hence, option A is ruled out. If AC =
10 cm, AB will become the largest side and ∠C the largest angle. But ∠C = 59°. Hence option B is ruled out. So,
AC is either 14 cm or 16 cm. In any case, ∠B will be the largest angle and ∠A (say Θ) the smallest:
Also, ∠B = 180° – (59° + Θ) = 121° – Θ
By sine formula
∴ sin (121° – Θ) ≈ sin (120° – Θ) = sin 120° cos Θ – cos120° sin Θ
Hence, option C is correct.
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Community Answer
Directions: Kindly study the following Question carefully and choose t...
Given Data:
- Length of side AB = 12 cm
- Length of side BC = 8 cm
- Angle C = 59°
Calculating Side AC using Law of Cosines:
- Using Law of Cosines, we have the formula: c² = a² + b² - 2ab * cos(C)
- Substituting the given values, we get: AC² = 12² + 8² - 2 * 12 * 8 * cos(59°)
- Calculating the cosine value of 59°, we get: cos(59°) ≈ 0.5299
- Plugging in the values, we get: AC² = 144 + 64 - 192 * 0.5299
- Simplifying further, we get: AC² = 144 + 64 - 101.8368
- Therefore, AC² ≈ 106.1632
- Taking the square root of both sides, we get: AC ≈ √106.1632 ≈ 10.305
Final Answer:
Therefore, the length of side AC is approximately 10.3 cm. Hence, option 'C' (14) is the correct answer.
- Length of side AB = 12 cm
- Length of side BC = 8 cm
- Angle C = 59°
Calculating Side AC using Law of Cosines:
- Using Law of Cosines, we have the formula: c² = a² + b² - 2ab * cos(C)
- Substituting the given values, we get: AC² = 12² + 8² - 2 * 12 * 8 * cos(59°)
- Calculating the cosine value of 59°, we get: cos(59°) ≈ 0.5299
- Plugging in the values, we get: AC² = 144 + 64 - 192 * 0.5299
- Simplifying further, we get: AC² = 144 + 64 - 101.8368
- Therefore, AC² ≈ 106.1632
- Taking the square root of both sides, we get: AC ≈ √106.1632 ≈ 10.305
Final Answer:
Therefore, the length of side AC is approximately 10.3 cm. Hence, option 'C' (14) is the correct answer.
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Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer?
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Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer?.
Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer?.
Solutions for Directions: Kindly study the following Question carefully and choose the right answer:The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC.a)12b)10c)14d)16Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
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