A triangle has sides A, B, and C. The angle between sides A and B is $(5pi)/12$ and the angle between sides B and C is $pi/12$ . If side B has a length of 9, what is the area of the triangle?

Question

1600 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-10T04:26:21

$10.8$

We can compute the third angle with the other two angles as the sum of the angles in a triangle is $180^circ$

$"Third angle"=180-(75+15)=180-90=90^circ$

As the triangle contains a $"right angle"$ ,we can use trigonometry

enter image source here

We need to find one more side to find the area of the triangle

So, we can use

$color(orange)(tan(theta)=("opposite") /(" hypotenuse")$

$rarrtan(a)=A/9$

$rarrtan(15)=A/9$

$rarr0.267=A/9$

$rarrA=0.267*9$

$rArrcolor(green)(A=2.4$

enter image source here

We can calculate the area of the triangle

$color(blue)("Area of triangle"=1/2*h*b$

Where,

$color(red)(h="height"=2.4$

$color(red)(b=base=9$

$:."Area"=1/2*2.4*9$

$rarr1/cancel2^1*cancel2.4^1.2*9$

$rarr1.2*9$

$rArrcolor(green)(10.8$

A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12(5pi)/12 and the angle between sides B and C is pi/12pi/12. If side B has a length of 9, what is the area of the triangle?