Question

If the angles of a triangle are `30^0a n d45^0` and the included side is `(sqrt(3)+1)c m` then the area of the triangle is______.

Answer 1

Traiangle with given specification is drawn in the following figure.

To find area of the triangle ABC, we need to find the length of altitude AD.
Now, in triangle ADC,
`tan30^(@)=h/(CD)`
`rArr CD=h cot30^(@)=sqrt3h`
In triangle ADB,
`tan45^(@)=h/(BD)`
`rArr BD=h cot 45^(@)=h`
Now, `Bc=BD+DC`
`:. h=sqrt3h=sqrt3+1`
`:. h=1`
`:. " Area of triangle "ABC=1/2xxADxxBC=(sqrt3+1)/2 cm^2`