Approximate area of the triangle below?

Step-by-step

This question expects a choice out of the four answers.

We can reason it as follows:

If the angles had been 90-45-45, then the triangle would be isosceles with each leg equal to 14, and the area would be 14*14/2 =  192/2 = 96.

Now one of the base angles has been reduced from 45 to 35 (still assuming a right triangle), the other leg can only diminish, and therefore the area is LESS than 96.

We also realize that changing from 90 to 95 degrees will not change the area by a whole lot, so we are looking for a number LESS than 96, the only of which is 72.8.

The exact value, by solving the triangle,

the opposite side of 35 degrees is 10.483 (using sine rule), and

the area is 73.378 (using A=(1/2)a*b*sin(C), not far from 72.8, if we are looking for the exact value.