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02 Jul 2021, 02:45
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C
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Difficulty:
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Question Stats:
83% (02:05) correct
17%
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Not Attempted Yet
What is the value of x in the figure above?
A. 4
B. 5
C. 6
D. 7
E. 8
Attachment:
2021-06-17_22-35-28.png [ 30.94 KiB | Viewed 5082 times ]
02 Jul 2021, 04:39
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Side of the triangle marked with x will be 10 as Triangle is an isosceles triangle
and other triangle is 30, 60, 90 degree triangle with base equal to 8/4 = 2; hence x = 10-4 =6 Option C
and other triangle is 30, 60, 90 degree triangle with base equal to 8/4 = 2; hence x = 10-4 =6 Option C
Bunuel
02 Jul 2021, 05:04
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We could have isoceles triangle with angles 40, 70, 70.
The length of whole side is 10 (split into x, 10-x) with hypotenuse = 8
We know that (10-x)/8 = sin(50), which is reduced to estimating sin(50) now.
We know that sin(50) > sin(45) = sqrt(2)/2 = 1.4/2 = 0.7
A. x = 4 -> 10-x = 6 -> sin50 = 6/8 = 0.75
B. x = 5 -> 10-x = 5 -> sin50 = 5/8 = 0.6x
C. x = 6 -> 10-x = 4 -> sin50 = 4/8 = 0.5
D. x = 7 -> 10-x = 3 -> sin50 = 3/8 = 0.3x
E. x = 8 -> 10-x = 2 -> sin50 = 2/8 = 0.25
Hence, we eliminated B-C-D-E, only option left is A.
(Honestly cannot do this within 2 mins, and not sure whether there are methods without trigonometry)
The length of whole side is 10 (split into x, 10-x) with hypotenuse = 8
We know that (10-x)/8 = sin(50), which is reduced to estimating sin(50) now.
We know that sin(50) > sin(45) = sqrt(2)/2 = 1.4/2 = 0.7
A. x = 4 -> 10-x = 6 -> sin50 = 6/8 = 0.75
B. x = 5 -> 10-x = 5 -> sin50 = 5/8 = 0.6x
C. x = 6 -> 10-x = 4 -> sin50 = 4/8 = 0.5
D. x = 7 -> 10-x = 3 -> sin50 = 3/8 = 0.3x
E. x = 8 -> 10-x = 2 -> sin50 = 2/8 = 0.25
Hence, we eliminated B-C-D-E, only option left is A.
(Honestly cannot do this within 2 mins, and not sure whether there are methods without trigonometry)
