Posted by **ken** on Wednesday, June 9, 2010 at 8:55am.

In triangle ABC, BC=40m , AB=50m and Angle A=53 degree. Determine the area of a triangle.

- geometry -
**Reiny**, Wednesday, June 9, 2010 at 9:11am
find angle C first of all

sinC/50 = sin53/40

sinC=.99829

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°

Case 1

AB=50

BC=40

angle B = 40.35

area = (1/2)(50)(40)sin40.35

= 647.41

Do the second case in the same way, you should get 554.16

- geometry -
**drwls**, Wednesday, June 9, 2010 at 9:16am
According to the law of sines,

40/sin 53 = 50/sin C

Therefore

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

- geometry -
**drwls**, Wednesday, June 9, 2010 at 9:21am
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

## Related Questions

- 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. ...
- Geometry - Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are...
- 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...
- maths - AD is the median of triangle ABC and G divides AD in the ratio 2:1 ....
- 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...

More Related Questions