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Two sides of a triangle and their included angles are 4cm, 5cm and 30d

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Two sides of a triangle and their included angles are 4cm, 5cm and 30d  [#permalink]

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New post 19 Nov 2011, 08:12
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:29) correct 39% (01:24) wrong based on 43 sessions

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Two sides of a triangle and their included angles are 4cm, 5cm and 30 degree resp. What is the are

A 10
B 15
C 5
D 20

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Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d  [#permalink]

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New post 21 Nov 2011, 08:56
1
cleetus wrote:
Two sides of a triangle and their included angles are 4cm, 5cm and 30degree resp. What is the are

A 10 B 15 C 5 D 20


Take the side of length 5 as your base. When you draw a height using this base, you will get a 30-60-90 triangle with a hypotenuse of 4. Since the short side in this triangle is our height, and since the short side in a 30-60-90 triangle is half the hypotenuse, the height is 2. So the area is 5*2/2 = 5.

A bit easier to see with a diagram of course.
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Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d  [#permalink]

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New post 11 Sep 2017, 10:48
Two sides of a triangle and their included angles are 4cm, 5cm and 30 degree resp. What is the area.

Please check attached image for detailed figure and explanation (ignore my handwriting :P)

Option 1: If we see 5 and 4 as sides, we usually go with right triangle and find 3rd side with Pythagoras theorem.
so 3rd side here = 3 . And area becomes 1/2 *4*3 =6
But its wrong answer as for right triangle 3,4,5 the angle between sides 5 and 4 is not 30 degree.
(Here non of the option is 6 so most likely we will not make this mistake)

Option 2: (Check attached img for diagram)
If we consider 5cm as base, we can draw a triangle using 4cm as 1 side and angle 30degree between them .
To find height of triamgle, drop perpendicular from 4cm side on 5cm base. Height can be calculated as we know angle = 30 degree.
So height = sin30 * 4cm = 2
so Area = 1/2 *5*2 = 5

Answer: C

Option 3: Using formula

Area formula if we know 2 sides of triangle and the angle between them =>

\(Area = \frac{a*b* Sin C}{2}\)
\(Area =\frac{4*5*Sin30}{2}\)

Area = 4*5*(1/2) /2 = 5

Answer: C

Attachments

Triangel with sides and angle.jpg
Triangel with sides and angle.jpg [ 1.63 MiB | Viewed 901 times ]

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Two sides of a triangle and their included angles are 4cm, 5cm and 30d  [#permalink]

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New post 28 Oct 2018, 12:21
IanStewart wrote:
cleetus wrote:
Two sides of a triangle and their included angles are 4cm, 5cm and 30degree resp. What is the are

A 10 B 15 C 5 D 20


Take the side of length 5 as your base. When you draw a height using this base, you will get a 30-60-90 triangle with a hypotenuse of 4. Since the short side in this triangle is our height, and since the short side in a 30-60-90 triangle is half the hypotenuse, the height is 2. So the area is 5*2/2 = 5.

A bit easier to see with a diagram of course.



HI IanStewart,
What am I missing ? If the height is 2 and the base is 5 and its a right Triangle, then Hypotenuse should be
\(\sqrt{(2^2 +5^2)}\) =\(\sqrt{29}\) but here we have 4. How ?
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Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d  [#permalink]

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New post 28 Oct 2018, 20:38
Two sides of a triangle and their included angles are 4cm, 5cm and 30 degree resp. What is the are
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Re: Two sides of a triangle and their included angles are 4cm, 5cm and 30d   [#permalink] 28 Oct 2018, 20:38
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