find angle C first of all
sinC/50 = sin53/40
angle C = 86.65° or 93.35° (we have the ambiguous case, you can actually draw two triangles satisfying your information.
then angle B = 40.35° or 33.65°
angle B = 40.35
area = (1/2)(50)(40)sin40.35
Do the second case in the same way, you should get 554.16
According to the law of sines,
40/sin 53 = 50/sin C
sin C = (50/40)*sin53 = 0.998
C = 86.7 degrees
B = 180 - 53 - 86.7 = 40.3 degrees
With all sides and all angles, you can solve for the area. If you pick AC as the base,
Area = (AC)*(1/2)*(BC)*sin 86.7
= 50*(0.5)*40*.998 = 998 m^2
Since my numbers don't agree with Reiny's, check mine for mistakes. Reiny is right about there being two cases. I assumed all acute angles
Answer this Question
Geometry - Please answer at least one . PLEASE 1. Triangle XYZ has a right ...
Math(Geometry) - In the diagram below(no diagram but details will be provided), ...
Geometry - Given: X, Y, and Z are the midpoints of teh sides of triangle ABC. ...
maths-urgently needed - In right angled triangle ABC angle B=90 degree and AB= ...
geometry - 1. Triangle ABC has a 63.0-degree angle at B, and side AC is 13.6 cm ...
college geometry - Given: right triangle ABC with right angle at C, AC=22 and BC...
geometry - Triangle ABC is a right triangle such that m angle B= 90 degrees. If ...
geometry - In triangle ABC, DE is parallel to AB. If DE is one-fifth AB, what is...
help math - In triangle ABC, points D,E,F are on sides BC,CA,AB respectively ...
Trigonometry/Geometry - In most geometry courses, we learn that there's no such ...