A triangle has sides A,B, and C. If the angle between sides A and B is $(5pi)/8$ , the angle between sides B and C is $pi/12$ , and the length of B is 3, what is the area of the triangle?

Question

1760 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-06T16:01:19

Area $= 1.356" units" ^2$ to 3 decimal places

Tony B

$color(blue)("Method")$

Find h using the sin rule. Then use h to determine the area.

$color(blue)("Solution")$

Target is to be able to apply $C/(sin(c))=B/(sin(b))$

To do this we need to find $/_cba$

The sum of the internal angles in a triangle is $180^o$

$=> /_cba=pi-(5pi)/8-(pi)/12=(7pi)/24" " (52.5 ^o)$

Thus we have

$C/(sin((5pi)/8)) = 3/(sin((7pi)/24))$

$C= 3 xxsin((5pi)/8)/(sin((7pi)/24))$

$h= C sin(pi/12)$

$h= 3 xxsin((5pi)/8)/(sin((7pi)/24))xxsin(pi/12)$

$Area = B/2xxh" "=" "9/2 xxsin((5pi)/8)/(sin((7pi)/24))xxsin(pi/12)$

$9/2xx(sin(112.5^o))/(sin(52.5^o))xxsin(15^o)$

$=1.356 " units"^2$

A triangle has sides A,B, and C. If the angle between sides A and B is (5pi)/8(5pi)/8, the angle between sides B and C is pi/12pi/12, and the length of B is 3, what is the area of the triangle?