Question

A triangle has two corners with angles of `( pi ) / 2` and `( 5 pi )/ 12`. If one side of the triangle has a length of `7`, what is the largest possible area of the triangle?

Answer 1

`=6.125`

Explanation:

Clearly this is a right-angled triangle since one of the two given angles is`=pi/2`
Therefore the third angle `=pi-(pi/2+(5pi)/12)=pi-(11pi)/12=pi/12`

In this right angled triangle side`=7` is hypotenuse

Therefore the other sides are

`height=7sin(pi/12)` and

`base=7cos(pi/12)`
Therefore

Area of the triangle

`=1/2times height times base`

`=1/2times7sin(pi/12)times 7cos(pi/12)`

`=1/2times7(0.2588)times 7(0.966)`

`=6.125`