Question

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?

Answer 1

`10.8`

Explanation:

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

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`

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`