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 54, 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 54, what is the area of the triangle?

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Answer 1 · 2017-03-15T02:15:19

The area of the triangle is about $390.69 u n i t s^{2}$ $390.69 units^2$

Explanation:

since $\frac{π}{2} = 90$ $pi/2=90$ degrees we know this triangle is right
we can find the side of A by saying $tan (\frac{π}{12}) = \frac{A}{54}$ $tan(pi/12)=A/54$
then rearrange the equation to get $A = 54 tan (\frac{π}{12})$ $A=54tan(pi/12)$
this gives you $A = 14.47$ $A=14.47$
then you can use the formula for the area of a triangle which is
$\frac{1}{2}$ $1/2$ (base)(height)
so the equation would be $\frac{1}{2} (54) (14.47)$ $1/2(54)(14.47)$
This is equal to (390.69)

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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 54, 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 54, what is the area of the triangle?