A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/4$ and the angle between sides B and C is $pi/6$ . If side B has a length of 12, what is the area of the triangle?

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Answer 1 · 2016-05-07T10:49:26

area of triangle is $(1/2)$ (base)(height) = $(1/2)*A*B$
= $(1/2)$ (12) $((12/(sin60π))*sin30º)$

Working in degree, π = 180º,

The Angle between C and A is
$(180º -90º -30º)$ = 60º

Hence using sine rule,

$A/sin(angle between B&C)$ = $B/sin(angle between C&A)$ =
$C/sin(angle betwen A&B)$

And given that $angle between AB$ is a right angle,

you need to only find A where

$A/sin(angle between B&C)$ = $B/sin(angle between C&A)$ ,

$A= (B/sin(angle between C&A))*sin(angle between B&C)$

= $(12/(sin60π))*sin30º$

Hence, area of triangle is $(1/2)$ (base)(height) = $(1/2)*A*B$
= $(1/2)$ (12) $((12/(sin60π))*sin30º)$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4(pi)/4 and the angle between sides B and C is pi/6pi/6. If side B has a length of 12, what is the area of the triangle?