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The leftmost triangle has two angles labeled 40° and 70°

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The leftmost triangle has two angles labeled 40° and 70° [#permalink] New post 17 Sep 2017, 11:45
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Question Stats:

66% (00:39) correct 33% (00:37) wrong based on 6 sessions


Attachment:
triangles.jpg
triangles.jpg [ 36.21 KiB | Viewed 881 times ]


Quantity A
Quantity B
X
6


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The leftmost triangle has two angles labeled 40° and 70° [#permalink] New post 27 Sep 2017, 11:01
how can we solve this?
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Re: The leftmost triangle has two angles labeled 40° and 70° [#permalink] New post 27 Sep 2017, 13:32
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Quote:
The leftmost triangle has two angles labeled 40° and 70°. Subtract these from 180° (the sum of the angles in any triangle) to determine that the third angle is 70°. Subtract 130 – 70 = 60° to get the measure of the adjoining angle in the rightmost triangle. Since the leftmost triangle is isosceles, the two long sides are each equal to 10. Since the rightmost triangle is a 30–60–90 triangle, the sides are in the proportion \(x: \sqrt{3} x : 2x\)

Because the hypotenuse is 8 and also the 2x in the ratio, the shortest leg of this triangle is x = 4. To calculate x, subtract: 10 – 4 = 6. The two quantities are equal.


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Re: The leftmost triangle has two angles labeled 40° and 70° [#permalink] New post 27 Sep 2017, 21:32
Carcass wrote:

Quantity A
Quantity B
X
6


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Now consider the triangle ABC(diag. attached)

We have

angle B = 70 and angle A = 40

Therefore angle C = 70 (180-(40+70)).

Since angle b = angle c

therefore side AB= side AC = 10.

Now consider the triangle GFC

angle G = 90, and angle C in this triangle = 60 (130 -70 , in triangle ABC, angle C= 70)

and angle F = 30 (180 - (90+60)). NOw we have a 30-60-90 triangle.

Side CF = 8, therefore by 30-60-90 triangle properties ( sides distribute in the ratio = 1:\(\sqrt{3}\) :2)

We have GF = \(4\sqrt{3}\) and GC = 4.

Now to find AG, we know

AG = AC- GC

or AG = 10 -4 = 6.
Attachments

triangles.jpg
triangles.jpg [ 23.69 KiB | Viewed 779 times ]


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Re: The leftmost triangle has two angles labeled 40° and 70°   [#permalink] 27 Sep 2017, 21:32
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