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 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 $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 15, what is the area of the triangle?

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Answer 1 · 2016-08-07T09:14:32

$= 30$ $=30$

Explanation:

This is a right angled triangle where $B = 15$ $B=15$
Therefore
Angle between $A$ $A$ and $C$ $C$ is $π - (\frac{π}{2} + \frac{π}{12}) = 5 \frac{π}{12}$ $pi-(pi/2+pi/12)=5pi/12$
$\frac{A}{sin (\frac{π}{12})} = \frac{B}{sin (5 \frac{π}{12})}$ $A/sin(pi/12)=B/sin(5pi/12)$
or
$\frac{A}{sin (\frac{π}{12})} = \frac{15}{sin (5 \frac{π}{12})}$ $A/sin(pi/12)=15/sin(5pi/12)$
or
$A = \frac{15}{sin (5 \frac{π}{12})} (\frac{sin π}{12})$ $A=15/sin(5pi/12)(sin pi/12)$
or
$A = 15 (0.268)$ $A=15(0.268)$
or
$A = 4$ $A=4$
Therefore
Area of the triangle $= \frac{1}{2} (15) (4)$ $=1/2(15)(4)$
$= \frac{60}{2}$ $=60/2$
$= 30$ $=30$

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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 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 $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 15, what is the area of the triangle?