# geometry

posted by .

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

• geometry -

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 -

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 -

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

## Similar Questions

1. ### Geometry

Given: X, Y, and Z are the midpoints of the sides of triangle ABC. Find rhe ratio of the area of triangle XYZ to the area of triangle ABC
2. ### geometry

1. Triangle ABC has a 63.0-degree angle at B, and side AC is 13.6 cm long. What is the diameter of the circle circumscribed about ABC?
3. ### Math(Geometry)

In the diagram below(no diagram but details will be provided), right triangle ABC and line BD is an altitude to side line AC. * Prove that (AB)^2=(AC)(AD) -When you label the triangle B should be were the right angle is C should be …
4. ### college geometry

Given: right triangle ABC with right angle at C, AC=22 and BC=6.Draw altitude CD where D is o hypotenuse AB. What is the ratio of the area of triangle ADC to the area of triangle CDB?
5. ### maths-urgently needed

In right angled triangle ABC angle B=90 degree and AB= root 34 unit. The coordinates of point B and Care (4,2)and (-1,y) respectively. If area of triangle ABC = 17 sq.units, then find value of y.
6. ### Geometry

Please answer at least one . PLEASE 1. Triangle XYZ has a right angle at Y. V,W are on XZ such that XV=XY. WZ=YZ, find ANGLE VYW . 2. STUVWXYZ is a regular octagon. Find SW/ TZ. 3. The interior angles of a convex polygon form an arithmetic …
7. ### Geometry

Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch the remainder of the figure. It will help if (triangle) …
8. ### maths

AD is the median of triangle ABC and G divides AD in the ratio 2:1 .Prove that area (triangle AGB )= area (triangle BGC )=area (triangle AGC )=1Ã·3area (triangle ABC )
9. ### maths

DRAW LOCUS OF POINT SO THAT IT IS EQUIDISTANT FROM BC & CA . ... constructed such that none of these triangles overlaps triangle ABC. a) Draw a triangle ABC and then sketch ... 16) AB = 3.2cm BC = 8.4cm The area of the triangle ABC …
10. ### math

If lines AB=6cm, AC=10cm, BC=2•4cm, CD=4cm and AD=X cm. Also angle ABC = angle ACD. (a).Prove that triangle ABC is similar to triangle ACD. (b).Determine the area of the quadrilateral ABCD if the area of triangle ACD is 60cm^2

More Similar Questions