A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 9, 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 $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 9, what is the area of the triangle?

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Answer 1 · 2016-08-12T09:00:47

$= 10.85$ $=10.85$

Explanation:

Clearly this is a right-angled triangle where $b a s e = B = 9$ $base= B=9$ and angle between $A$ $A$ and $C$ $C$ = $π - (\frac{π}{2} + \frac{π}{12}) = π - (\frac{7 π}{12}) = \frac{5 π}{12}$ $pi-(pi/2+pi/12)=pi-((7pi)/12)=(5pi)/12$
Therefore we can write
$\frac{B}{A} = tan (\frac{5 π}{12})$ $B/A=tan((5pi)/12)$
or
$\frac{9}{A} = 3.73$ $9/A=3.73$
or
$A = \frac{9}{3.73}$ $A=9/3.73$
or
$A = 2.41$ $A=2.41$ (Pl.note $A$ $A$ is the $h e i g h t$ $height$ )
Area of the triangle $= \frac{1}{2} \times h e i g h t \times b a s e = \frac{1}{2} \times 2.41 \times 9 = 10.85$ $=1/2times height timesbase=1/2times2.41times9=10.85$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 9, 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 π2(pi)/2 and the angle between sides B and C is π12pi/12. If side B has a length of 9, 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 $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 9, what is the area of the triangle?