A triangle has two corners with angles of $( pi ) / 2$ and $( 5 pi )/ 12$ . If one side of the triangle has a length of $7$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $( pi ) / 2$ and $( 5 pi )/ 12$ . If one side of the triangle has a length of $7$ , what is the largest possible area of the triangle?

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Answer 1 · 2016-08-16T16:58:49

$=6.125$

Explanation:

Clearly this is a right-angled triangle since one of the two given angles is $=pi/2$
Therefore the third angle $=pi-(pi/2+(5pi)/12)=pi-(11pi)/12=pi/12$

In this right angled triangle side $=7$ is hypotenuse

Therefore the other sides are

$height=7sin(pi/12)$ and

$base=7cos(pi/12)$
Therefore

Area of the triangle

$=1/2times height times base$

$=1/2times7sin(pi/12)times 7cos(pi/12)$

$=1/2times7(0.2588)times 7(0.966)$

$=6.125$

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A triangle has two corners with angles of $( pi ) / 2$ and $( 5 pi )/ 12$ . If one side of the triangle has a length of $7$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A triangle has two corners with angles of ( pi ) / 2 ( pi ) / 2 and ( 5 pi )/ 12 ( 5 pi )/ 12 . If one side of the triangle has a length of 7 7 , what is the largest possible area of the triangle?

1 Answer

Explanation:

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Impact of this question

A triangle has two corners with angles of $( pi ) / 2$ and $( 5 pi )/ 12$ . If one side of the triangle has a length of $7$ , what is the largest possible area of the triangle?