A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 15, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 15, what is the area of the triangle?

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Answer 1 · 2016-08-11T20:40:31

$= 28.13$ $=28.13$

Explanation:

The angle between $A$ $A$ and $C$ $C$ $= π - (\frac{5 π}{12} + \frac{π}{12}) = π - \frac{π}{2} = \frac{π}{2}$ $=pi-((5pi)/12+pi/12)=pi-pi/2=pi/2$
This shows that triangle is right-angled with hypotenuse $= B = 15$ $=B=15$
Hence $h e i g h t =$ $height=$ side $A = 15 sin (\frac{π}{12})$ $A=15sin(pi/12)$ and $b a s e =$ $base=$ side $B = 15 cos (\frac{π}{12})$ $B=15cos(pi/12)$
Therefore Area of the triangle $= \frac{1}{2} \times h e i g h t \times b a s e$ $=1/2times height times base$
$= \frac{1}{2} \times 15 sin (\frac{π}{12}) 15 cos (\frac{π}{12})$ $=1/2times15sin(pi/12)15cos(pi/12)$
$= \frac{225}{2} (0.2588) (0.966)$ $=225/2(0.2588)(0.966)$
$= 28.13$ $=28.13$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 15, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 15, what is the area of the triangle?