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

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

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Answer 1 · 2016-08-16T16:58:49

$= 6.125$ $=6.125$

Explanation:

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

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

Therefore the other sides are

$h e i g h t = 7 sin (\frac{π}{12})$ $height=7sin(pi/12)$ and

$b a s e = 7 cos (\frac{π}{12})$ $base=7cos(pi/12)$
Therefore

Area of the triangle

$= \frac{1}{2} \times h e i g h t \times b a s e$ $=1/2times height times base$

$= \frac{1}{2} \times 7 sin (\frac{π}{12}) \times 7 cos (\frac{π}{12})$ $=1/2times7sin(pi/12)times 7cos(pi/12)$

$= \frac{1}{2} \times 7 (0.2588) \times 7 (0.966)$ $=1/2times7(0.2588)times 7(0.966)$

$= 6.125$ $=6.125$

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