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05 Feb 2015, 08:58
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C
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60% (02:06) correct
40%
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wrong
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In triangle ABC, angle ABC is 105 degrees. Is the area of triangle ABC less than 5?
(1) Segment AB = 2√2
(2) Angle BCA is 30 degrees.
(1) Segment AB = 2√2
(2) Angle BCA is 30 degrees.
05 Feb 2015, 19:54
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(1) Not sufficient.
(2) Not sufficient. Just knowing the values of all angles does not allow us to find the area.
(1)+(2) Sufficient. From (1) we know that AB is 2√2, so if we spit the triangle ABC into two triangles drawing a line from the angle ABC, we can get a two special right triangles. First triangle 45-45-90 with a hypotenuse 2√2 and the second triangle 30-60-90. From that point we can find all the needed values.
Answer C
(2) Not sufficient. Just knowing the values of all angles does not allow us to find the area.
(1)+(2) Sufficient. From (1) we know that AB is 2√2, so if we spit the triangle ABC into two triangles drawing a line from the angle ABC, we can get a two special right triangles. First triangle 45-45-90 with a hypotenuse 2√2 and the second triangle 30-60-90. From that point we can find all the needed values.
Answer C
25 Aug 2015, 13:22
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I don't think we require splitting and spend time on it. Once we know all three angles and length of one side, other sides can be known through the ratio of these angles. However it is not essential but the formula to find the lengths is a/sin A = b/Sin B = c/Sin C
