Triangle: Similar Side Lengths, Different Angles

Question

If two triangles ABC and DEF have the same area, with AB=DE and AC=DF, and the measure of an angle A = 43 degrees, what is the measure of angle D if angle D is obtuse? So far I've understood that if 1/2 AB * AC * sin (43) = 1/2 DE * DF * sin D, then sin(43) must equal to sin D. After that I'm stuck because angle D has to be obtuse...

Answer 1

In general, if Z is a positive number not exceeding 1, then θ = arcsin Z gives you an angle in the first quadrant (an acute angle).

 

There's another angle, in quadrant two, that also has the identical sine value, and this will be 180^o - θ (obtuse!).

 

Got it?