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Triangle ABC is an obtuse, isosceles triangle in which the length of s

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Sajjad1994
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Triangle ABC is an obtuse, isosceles triangle in which the length of s [#permalink] New post   Updated on: 01 Oct 2023, 03:23
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Triangle ABC is an obtuse, isosceles triangle in which the length of side AC is greater than the length of side BC. From the table below, select values that could correspond to the measures of angle B and angle C.
Measure of
angle B 		Measure of
angle C 		---------
30
38
60
68
104
106
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Measure of
angle B: 104 Measure of
angle C: 38

Originally posted by Sajjad1994 on 09 Aug 2020, 06:40.
Last edited by BottomJee on 01 Oct 2023, 03:23, edited 2 times in total.
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Re: Triangle ABC is an obtuse, isosceles triangle in which the length of s [#permalink] New post   05 Jan 2021, 07:58
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sthahvi wrote:
can someone explain the answer


Explanation

An obtuse angel is one which is always greater than 90 degree but less than 180. The triangle is also an isosceles which means that two angel of the triangle are equal in length. We know that side AC is greater than BC (A rough figure is below)

Attachment:
123.jpg
123.jpg [ 25.57 KiB | Viewed 2135 times ]


If angel AC is greater than BC it means angel B is the one which is greater than 90. Now we have to select the corresponding angels. We know angel B is greater than 90 so only two option left for B. If we pick up 106 for B then the remaining angel will be 37 degree each which not available in the options. Next available option for B is 104, If B is 104 then the remaining both will equal to 38 and it is available in the options so B=104 and C=38

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Re: Triangle ABC is an obtuse, isosceles triangle in which the length of s [#permalink] New post   20 Jun 2021, 09:45
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If the length of side AC is greater than that of BC, then the sides, AB & BC, are of equal length (Since ABC is an isosceles triangle). So, \(\angle\) A = \(\angle\) C = x & \(\angle\) B>\(90^{\circ}\) = y (since ABC is also an obtuse angled triangle). Kindly refer the image.

So, y+2x = 180.....eq-1

There are only two values (104 & 106) greater than 90, so only those values can be the value of y. Substututing those values in eq-1, we get:

Option-1: y=104 & x=38, or
Option-2: y=106 & x=37

Only the corresponding values of Option-1, satisfies the answer options. Hence, the correct answer.
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Re: Triangle ABC is an obtuse, isosceles triangle in which the length of s [#permalink] New post   04 Jan 2021, 04:38
can someone explain the answer
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Re: Triangle ABC is an obtuse, isosceles triangle in which the length of s [#permalink] New post   06 Jan 2021, 02:16
B > 90 and C=A ... if C=A= 30 B= 90 ... so it become an isosceles right triangle. If C=A=38 B will 104.... Option B is correct .
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Re: Triangle ABC is an obtuse, isosceles triangle in which the length of s [#permalink]
06 Jan 2021, 02:16
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