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What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150o?
- a)24 sq units
- b)48 sq units
- c)24√3
- d)48√3
- e)Such a triangle does not exist
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the area of an obtuse angled triangle whose two sides are 8 an...
If two sides of a triangle and the included angle 'y' is known, then the area of the triangle = 1/2 * (Product of sides) * sin y
Substituting the values in the formula, we get 1/2 * 8 * 12 * sin 150o
Substituting the values in the formula, we get 1/2 * 8 * 12 * sin 150o
Most Upvoted Answer
What is the area of an obtuse angled triangle whose two sides are 8 an...
To find the area of an obtuse angled triangle, we can use the formula:
Area = (1/2) * a * b * sin(C)
where a and b are the lengths of the two sides and C is the angle included between the two sides.
In this case, a = 8, b = 12, and C = 150 degrees.
First, we need to convert the angle from degrees to radians since the sine function in the formula takes radians as input. We can use the formula:
radians = (pi/180) * degrees
So, radians = (pi/180) * 150 = 5pi/6.
Now, we can substitute the values into the formula:
Area = (1/2) * 8 * 12 * sin(5pi/6)
Simplifying further:
Area = (1/2) * 8 * 12 * sin(150 degrees)
Area = (1/2) * 8 * 12 * sin(5pi/6)
Area = 4 * 12 * sin(5pi/6)
Area = 48 * sin(5pi/6)
Since sin(5pi/6) = 1/2, we can substitute this value in:
Area = 48 * (1/2)
Area = 24
Therefore, the area of the obtuse angled triangle is 24 square units.
The correct answer is:
c) 24
Area = (1/2) * a * b * sin(C)
where a and b are the lengths of the two sides and C is the angle included between the two sides.
In this case, a = 8, b = 12, and C = 150 degrees.
First, we need to convert the angle from degrees to radians since the sine function in the formula takes radians as input. We can use the formula:
radians = (pi/180) * degrees
So, radians = (pi/180) * 150 = 5pi/6.
Now, we can substitute the values into the formula:
Area = (1/2) * 8 * 12 * sin(5pi/6)
Simplifying further:
Area = (1/2) * 8 * 12 * sin(150 degrees)
Area = (1/2) * 8 * 12 * sin(5pi/6)
Area = 4 * 12 * sin(5pi/6)
Area = 48 * sin(5pi/6)
Since sin(5pi/6) = 1/2, we can substitute this value in:
Area = 48 * (1/2)
Area = 24
Therefore, the area of the obtuse angled triangle is 24 square units.
The correct answer is:
c) 24
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What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150o?a)24 sq unitsb)48 sq unitsc)24√3d)48√3e)Such a triangle does not existCorrect answer is option 'A'. Can you explain this answer?
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What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150o?a)24 sq unitsb)48 sq unitsc)24√3d)48√3e)Such a triangle does not existCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150o?a)24 sq unitsb)48 sq unitsc)24√3d)48√3e)Such a triangle does not existCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150o?a)24 sq unitsb)48 sq unitsc)24√3d)48√3e)Such a triangle does not existCorrect answer is option 'A'. Can you explain this answer?.
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